www.aydinyayinlari.com.tr 11. SINIF DÜZGÜN ELEKTRİK ALAN VE SIĞA ³ Düzgün Elektrik Alan • 50 ³ Konu Testleri • 58 ³ Paralel Levhalar • 61 ³ Fen Lisesi Testleri • 65 ³ Sığa • 67 ³ Konu Testleri • 74 ³ Karma Testler • 87 ³ Fen Lisesi Karma Testler • 90 ³ Yazılı Soruları • 94 ³ Yeni Nesil Sorular • 96 1. ? 2. ? 49 1. ? 2. ?
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr %Ñ[HÑO&MFLUSJL\"MBO ÷MJöLJMJ,B[BONMBS 11.2.3.1. : :ÐLMÐ JMFULFOWFQBSBMFMMFWIBMBSBSBTOEBPMVõBOFMFLUSJLBMBO BMBO¿J[HJMFSJOJ¿J[FSFLB¿LMBS TANIM .qk(7$k, &MFLUSJL BMBO ¿J[HJMFSJ EBJNB + ZÐLMÐ MFWIB- /PLUBTBMCJSZÐLÐOFUSBGOEBFMFLUSJLTFMFULJTJOJ EBO - ZÐLMÐMFWIBZBEPóSVEVS HËTUFSEJóJCËMHFZFelektrik alanEFOJS %m/*m ÖRNEK 1 1BSBMFMJLJMFWIBBSBTOEBPMVõBO EÐ[HÐOFMFLUSJLBMBOBBJU¿J[HJMFS /PLUBTBMCJSZÐLFUSBGOEBPMVõBOFMFLUSJLBMBO E õFLJMEFLJHJCJEJS IFSOPLUBEBGBSLMZËOZBEBEPóSVMUVEBPMBCJMF- DFóJJ¿JOEÐ[HÐOCJSFMFLUSJLBMBOPMVõUVSNB[ #VOB HÌSF MFWIBMBSO ZFSJ- OJ ÀJ[FSFL FMFLUSJL ZÑLMFSJOJO &MFLUSJL BMBO Ë[FMMJLMFSJ IFS OPLUBEB BZO PMBO JöBSFUMFSJOJ MFWIBMBS Ñ[FSJOEF alanlara EÐ[HÐOFMFLUSJLBMBOEFOJS HÌTUFSJOJ[ + E- - &MFLUSJLBMBO + ZÑLUFO - ZÑ- +- +- E - LF EPôSV MFWIBMBSB EJL PMEVôVO- +- - EBOMFWIBMBSöFLJMEFLJHJCJEJS +- + +- + + V ÖRNEK 2 ±[EFõ JMFULFOWFQBSBMFMJLJMFWIB JMFULFOUFMMFSMFÐSFUF- DJO WF m LVUCVOBCBóMBOEóOEBPMVõBOFMFLUSJL ++ K -L BMBO ¿J[HJMFSJ õFLJMEFLJ HJCJEJS \"MBO ¿J[HJMFSJOJO EÐ[HÐO- ++ MÐóÐ MFWIBMBSO V¿ LTNMBSOEB CP[VMVS \"ODBL ¿Ë[ÐN - - - - -L ++ - ZBQMSLFO MFWIBMBS BSBTOEBLJ FMFLUSJL BMBO EÐ[HÐO LB- ++ - CVM FEJMJS &MFLUSJL BMBO ¿J[HJMFSJ MFWIB J¿JOEF CJSCJSMFSJOF ++ QBSBMFMEJS -K %m/*m -+ + \"MBO¿J[HJMFSJ ¿LULMBSWFTPOCVMEVLMBSZÐ[F- ZFEBJNBEJLUJS + + &MFLUSJLBMBO¿J[HJMFSJCJSCJSMFSJOFQBSBMFMWFFõJU + BSBLMLMBSMB¿J[JMFSFLNPEFMMFOJS + ZÑLMÑ,WF - ZÑLMÑ-MFWIBMBSBSBTOEB :ÐLMFOFO JLJ MFWIBOO QPUBOTJZFM GBSL ÐSFUF- PMVöBOEÑ[HÑOFMFLUSJLBMBOÀJ[HJMFSJOJHÌTUFSJOJ[ DJOLVUVQMBSBSBTOEBLJQPUBOTJZFMGBSLOBFõJU PMVS K -L -FWIBMBSBSBTOEBFMFLUSJLBMBOõJEEFUJ MFWIB- E - MBSBSBTOEBLJIFSOPLUBEBBZOES - - - - - -L -K -+ + + E+ + %Ñ[HÑO FMFLUSJL BMBO ÀJ[HJMFSJ CJSCJSJOF QBSBMFMEJS :ÌOÑ + ZÑLMÑMFWIBEBO - ZÑLMÑMFWIBZBEPôSVEVS 50
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF %m/*m ÖRNEK 4 ++++++ E öQJOVDVOBCBóMNLÐUMFMJ mq RZÐLMÐQBS¿BDóOQBSBMFM +q F + MFWIBMBSBSBTOEBLJEFOHF d –V LPOVNVõFLJMEFLJHJCJEJS E -FWIBMBSOLPOVNVOVWF F –q DJTNFFULJZFOLVWWFUMFSJ ¿J[FSFLHËTUFSJOJ[ ------ ¶SFUFDJO HFSJMJNJ 7 MFWIBMBS BSBT V[BLML E JTF + MFWIBMBS BSBTOEBLJ FMFLUSJL BMBO WFLUËSFMEJS WF CÐ- ZÐLMÐóÐ + E = V CBóOUTOEBOCVMVOVS + d F + + Birimi volt (v) EJS mq - metre (m) - mg E - &MFLUSJLBMBOJ¿JOEFLJZÐLMÐCJSDJTNFFULJFEFOLVW- -+ WFUJOCÐZÐLMÐóÐ - -V F = qE = q V JGBEFTJZMFCVMVOVS &MFLUSJLBMBOÀJ[HJMFSJ + MFWIBEBO - MFWIBZBEPô- d SVEVS$JTJNEÑöFZMFaBÀTZBQBSBLEFOHFMFOEJôJOF HÌSFZÑLJöBSFUJ - EJS .qk(7$k, + ZÐLMÐDJTNFFULJFEFOLVWWFU FMFLUSJLBMBO- ÖRNEK 5 MBBZOZËOMÐ - ZÐLMÐDJTNFFULJFEFOLVW- WFU FMFLUSJLBMBOMB[UZËOMÐEÐS:ÐLTÐ[QBS¿B- m kütleli +RZÐLMÐDJTJNôFLJM-IEFEFOHFEFEJS:ÐL- DLMBSB FMFLUSJL BMBOEB FMFLUSJL LVWWFUJ FULJ FU- MÐDJTJNôFLJM-IIEFQBSBMFMMFWIBMBSBSBTOEBHËTUFSJMFO NF[ LPOVNVBMZPS KL ÖRNEK 3 1BSBMFM MFWIBMBS BSBTOEBLJ mm BOBIUBSLBQBUMODBNLÐUMFMJ +q +q ip +R ZÐLMÐ DJTNF FULJZFO LVW- m WFUMFSJ¿J[FSFLHËTUFSJOJ[ AB +q ôFLJMmI ôFLJMmII +– #VOBHÌSF V * ¶SFUFDJO\"LVUCV + #LVUCV - JõBSFUMJEJS +- ** &MFLUSJLBMBO¿J[HJMFSJ,MFWIBTOEBO-MFWIBTOB a EPóSVEVS + +q - *** $JTNF FULJZFO FMFLUSJL LVWWFUJ WF FMFLUSJL BMBO WFL- + m- UËSMFSJBZOZËOMÐEÐS F JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS + mg - +R ZÑLMÑ DJTJN , MFWIBT UBSBGOEBO JUJMJS - MFWIBT UB- +– SBGOEBOÀFLJMJSTFõFLJM-IIEFLJHJCJEFOHFEFLBMS·SFUF- DJO\"LVUCV + #LVUCV - ZÑLMÑPMVS%PMBZTZMBFMFLU- V SJLBMBOÀJ[HJMFSJ,MFWIBTOEBO-MFWIBTOBEPôSVPMVS &MFLUSJLBMBOÀJ[HJMFSJ + MFWIBEBO - MFWIBZBEPô- +ZÑLMFSEF ' JMF E BZOZÌOMÑPMVS SVEVS + ZÑLMÑ DJTNF FULJZFO FMFLUSJLTFM LVWWFU FMFLUSJLBMBOJMFBZOZÌOMÑEÑS\"ZSDBDJTNFZFSÀFLJNJ :BOU* **WF*** LVWWFUJEFFULJFUNFLUFEJS 51 5. * **WF***
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr %Ñ[HÑO&MFLUSJL\"MBO ÷MJöLJMJ,B[BONMBS 11.2.3.2. : :ÐLMÐ JMFULFOWFQBSBMFMMFWIBMBSBSBTOEBPMVõBOFMFLUSJLBMBOOCBóMPMEVóVEFóJõLFOMFSJBOBMJ[FEFS %m/*m %m/*m EBSBMLMQBSBMFMMFWIBMBS 7QPUBOTJZFMGBSL- -FWIBMBSBSBTV[BLMLEZBQMQ QPUBOTJZFM OB TBIJQ ÐSFUFDF CBóMBOEóOEB MFWIBMBS BSB- TOEBLJ GBSL ÐSFUFDJO QPUBOTJZFMJOF FõJU PMBOB GBSL 7 PMBO ÐSFUFDF CBóMBOEóOEB MFWIBMB- LBEBS MFWIBMBS +R WF - q yükleri ile yükle- OJS-FWIBMBSBSBTOEB&CÐZÐLMÐóÐOEFFMFLU- SOZÐLÐZBSZBEÐõFSFL FMFLUSJLBMBOCÐZÐLMÐ- SJLBMBOPMVõVS óÐ E PMVS 2 + d - 2d + E - +- + - + +- - + E/2 - +q V –q +- + +– - +q 2 -q 2 V .qk(7$k, &MFLUSJL BMBO MFWIBMBS BSBTOEBLJ V[BLML JMF UFSTPSBOUMES %m/*m %m/*m -FWIBMBS BSBT E V[BLMó TBCJU UVUVMBSBL QP- 1BSBMFMMFWIBMBSCJSÐSFUFDFCBóMBOEóOEBMFW- UBOTJZFM GBSL 7 ZBQMEóOEB MFWIBMBSO ZÐLÐ IBMBSO QPUBOTJZFM GBSL TBCJUMFOJS -FWIBMBS JLJLBUBSUBSBLRPMVS:ÐLÐOBSUNBTFMFLUSJL ZÐLMFOEJLUFO TPOSB ÐSFUF¿UFO BZSMSTB MFWIB- BMBO¿J[HJMFSJOJTLMBõUSSWFFMFLUSJLBMBOCÐZÐL- MBSEBLJZÐLNJLUBSMBSTBCJULBMS MÐóÐ&PMVS %PMBZTZMBMFWIBMBSBSBTFMFLUSJLBMBO¿J[HJMFSJ- d OJOTBZTWFFMFLUSJLBMBOõJEEFUJEFóJõNF[ 2E + - d d +– +- +- + 2V - +- +- + - +- +- + - + E- + E- +2q -2q +- V ôFLJMmII ôFLJMmI .qk(7$k, -FWIBMBS ôFLJM-I EFLJ LPOVNEBO ôFLJM-II deki &MFLUSJLBMBO QPUBOTJZFMGBSLJMFEPóSVPSBOUM- LPOVNBHFUJSJMJZPS-FWIBMBSôFLJM-IIEFLJLPOVN- ES EBZLFOMFWIBMBSBSBTEV[BLMóBSUBSTB &MFLUSJLTFMLVWWFUMFSFLBSõJõZBQMS 4JTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJBSUBS -FWIBMBSBSBTOEBLJ7QPUBOTJZFMJBSUBS 52
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ÖRNEK 6 TANIM d &MFLUSJL BMBO J¿JOEFLJ ZÐLMÐ DJTNF FULJ FEFO +- +- FMFLUSJLTFMLVWWFUJOCÐZÐLMÐóÐ +- +- F = qE = q V EJS d :ÐLÐOCJSMFWIBEBOEJóFSJOFUBõONBTTSBTO- +- EBFMFLUSJLTFMLVWWFUMFSJOZBQUóJõ 8= F · d = q · E · d = q· V ·d =R7PMVS V d ôFLJMEFLJQBSBMFMMFWIBMBSCJSÐSFUFDFCBóMBOBSBLZÐLMF- d OJZPS #VOB HÌSF E V[BLMô BSUBSTB ÑSFUFDJO 7 QPUBOTJ- +- ZFMJ MFWIBMBSEB CJSJLFO R ZÑLÑ WF MFWIBMBS BSBTO- E EBPMVöBO&FMFLUSJLBMBOCÑZÑLMÑôÑOBTMEFôJöJS +- + +q - + F + -q - -F - -FWIBMBS ÑSFUFDF CBôM PMEVôV TÑSFDF 7 TBCJU LBMS 7TBCJULFOENFTBGFTJBSUBSTBMFWIBMBSEBCJSJLFOZÑL +- V V NJLUBSB[BMS4BCJUQPUBOTJZFMGBSLBMUOEBE = CB- .qk(7$k, %Ð[HÐOFMFLUSJLBMBOJ¿JOEF + WF - ZÐL- ôOUTOBHÌSFEBSUBSTB&B[BMS d MFSFFULJZFOFMFLUSJLTFMLVWWFUMFS[UZËOMÐEÐS ÖRNEK 7 ÖRNEK 8 d ôFLJMEFLJQBSBMFMMFWIBMBSCJSÐSFUFDFCBóMZLFO,MFW- +- IBTOOËOÐOEFOTFSCFTUCSBLMBO+RWF+ 2q yükleri- +- +- OFFULJZFOFMFLUSJLTFMLVWWFUMFS F 1 ve F 2 -MFWIBT- +- OOËOÐOEFOTFSCFTUCSBLMBO-q yüküne etkiyen elekt- ôFLJMEFLJQBSBMFMMFWIBMBSCJSÐSFUF¿MFZÐLMFOEJLUFOTPO- SJLTFMLVWWFU F 3 PMNBLUBES SBÐSFUF¿MFPMBOCBóMBOUTLFTJMJZPS #V EVSVNEB E NFTBGFTJ BSUSMSTB MFWIBMBSEB CJSJ- K+ d -L LFORZÑLÑ MFWIBMBSBSBT7QPUBOTJZFMGBSLWFMFW- E - IBMBSBSBTOEBPMVöBO&FMFLUSJLBMBOCÑZÑLMÑôÑOB- + TMEFôJöJS + +q F1 - F2 –F3 –q - ·SFUFÀMFWIBMBSEBOZÑLLBZCPMNBEBOÀLBSMEôOEBR + +2q EFôFSJTBCJULBMS EOJOBSUNBTRZÑLÑOÑFULJMFNF[ + - V +- EOJOBSUNBT7EFôFSJOJBSUSS E = CBôOUTOB V d HÌSFEWF7OJOCJSMJLUFBSUNBTZMB&EFôJöNF[ #VOBHÌSF F 1, F 2 ve F 3 BSBTOEBLJCÑZÑLMÑLT- SBMBNBTOFEJS :FS¿FLJNJËOFNTFONJZPS %m/*m '=R&CBôOUTOBHÌSF %Ð[HÐO FMFLUSJL BMBO J¿JOEF TFSCFTU CSBLMBO '1 =R& ZÐLMÐQBS¿BDLMBSZFS¿FLJNJOJOËOFNTFONFEJóJ '2 =R& PSUBNEBFMFLUSJLBMBO¿J[HJMFSJOFQBSBMFMIBSFLFU '3 = -R&ZB[MBSBL FEFS+RZÐLMÐQBS¿BDL + ZÐLMÐMFWIBEBO '2 >'1 ='3CVMVOVS - ZÐLMÐMFWIBZBEPóSVIBSFLFUFEFSLFO- q ZÐLMÐQBS¿BDL[UZËOEFIBSFLFUFEFS 6. 7EFôJöNF[ RB[BMS &B[BMS 7. REFôJöNF[ 7BSUBS &EFôJöNF[ 53 8. '2 '1 '3
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 9 %m/*m VX VY VZ +- E - + ip +- +- + +q F +- - a + mg - +- d +- +- V V ôFLJMEFLJ +R ZÐLMÐ DJTNJO QBSBMFM MFWIBMBS BSBTOEBLJ EFOHFLPOVNVHËTUFSJMJZPS:ÐLMÐDJTNFFULJZFOLVWWFU- &MFLUSJLTFMQPUBOTJZFM TLBMFSCJSCÐZÐLMÐLUÐS MFSJHËTUFSJOJ[ + ZÐLMÐMFWIBEBO - ZÐLMÐMFWIBZBHJEJM- q V EJL¿FQPUBOTJZFMB[BMS 79 >7Y >7ZPMVS F qE d tan a = = = )FSIBOHJCJSMFWIBZBFõJUV[BLMLUBPMBOOPLUB- MBSOFMFLUSJLQPUBOTJZFMMFSJFõJUPMVS mg mg mg &MFLUSJLQPUBOTJZFMMFSJOJOFõJUPMEVóVOPLUBMBSO qV PMVõUVSEVóV ZÐ[FZMFSF Fõ QPUBOTJZFM ZÐ[FZMFSJ tan a = EFOJS mgd ÖRNEK 10 ÖRNEK 11 + + X- + Y- + + Z- + - T + + E m iF + - - mg +- - -+ V - -V ôFLJMEFLJQBSBMFMMFWIBMBSCJSÐSFUFDFCBóMBOBSBLZÐLMFO- NJõUJS NLÐUMFMJZÐLMÐDJTNJOEÐ[HÐOFMFLUSJLBMBOJ¿JOEFLJEFO- #VOBHÌSF HFLPOVNVõFLJMEFLJHJCJEJS #VOBHÌSF * 9 : ;OPLUBMBSOOQPUBOTJZFMMFSJ79 >7Y >7ZEJS * $JTJN - ZÐLMÐEÐS ** NLÐUMFTJB[BMSTBiB¿TBSUBS ** 9 : ; OPLUBMBSOEBLJ FMFLUSJL BMBO CÐZÐLMÐLMFSJ *** RZÐLÐBSUBSTBiB¿TBSUBS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS E9 = E = EZEJS Y *** -FWIBMBS BSBT V[BLML B[BMSTB MFWIBMBS BSBTOEBLJ FMFLUSJLBMBOõJEEFUJBSUBS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS NLÑUMFMJDJTNFFULJZFOFMFLUSJLTFMLVWWFU ' , E JMF + ZÑLMÑ MFWIBEBO V[BLMBöULÀB QPUBOTJZFM B[BMS [UZÌOMÑEÑS:BOJDJTJN - ZÑLMÑEÑS$JTNJOLÑUMFTJ -FWIBMBS TBCJU QPUBOTJZFMF CBôMZLFO MFWIBMBS BSBT B[BMSTBDJTJNEBIBÀPLBÀMS iBÀTBSUBS FMFLUSJLBMBOTBCJUUJS '=R&CBôOUTOBHÌSFRBSUBSTB'BSUBS iBÀTBS- ENFTBGFTJOJOB[BMNBT FMFLUSJLBMBOÀJ[HJMFSJOJTLMBö- UBS:BOU* **WF*** USS FMFLUSJLBMBOöJEEFUJBSUBS :BOU* **WF*** qV 10. * **WF*** 54 11. * **WF*** 9. tan a = mgd
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF %Ñ[HÑO&MFLUSJL\"MBO ÷MJöLJMJ,B[BONMBS 11.2.3.3. : :ÐLMÐQBS¿BDLMBSOEÐ[HÐOFMFLUSJLBMBOOEBLJEBWSBOõOB¿LMBS %m/*m .qk(7$k, $JTNJO J[MFZFDFóJ ZËSÐOHFZJ FMFLUSJLTFM LVW- %Ð[HÐO FMFLUSJL BMBO J¿JOEFLJ ZÐLMÐ QBS¿BD- WFU JMF DJTNJO BóSMó BSBTOEBLJ CÐZÐLMÐL JMJõ- óB FULJ FEFO FMFLUSJLTFM LVWWFUJO CÐZÐLMÐóÐ LJTJCFMJSMFS F =R&CBóOUTOEBOCVMVOVS ÖRNEK 12 %Ð[HÐOFMFLUSJLBMBOJ¿JOEFZÐLTÐ[QBS¿BDLMB- SBJTFFMFLUSJLTFMLVWWFUFULJFUNF[ \"óSMóËOFNTFONFZFOZÐLMÐR1WFR2QBS¿BDLMBS- ++++++ OBFULJZFOFMFLUSJLTFMLVWWFUMFS F1 ve F2 õFLJMEFLJHJ- +q j1 CJEJS E + + F = qE + F1 - V- + q1 - j1 F2 - j + q2 - E j2 ------ +- \"óSMóËOFNTFONFZFO+RZÐLMÐDJTJNEÐõFZEÐ[MFN- V EFLJ ZÐLMÐ MFWIBMBSO BSBTOB FMFLUSJL BMBOB EJL PMBSBL BUMEóOEBZBUBZBUõIBSFLFUJZBQBS:BUBZBUõIBSFLF- #VOBHÌSF UJOEFZBUBZI[ j1 EFóJõNF[%ÐõFZEÐ[MFNEFDJTNF * R1 + R2 m ZÐLMÐEÐS FULJZFOFMFLUSJLTFMLVWWFUJOFULJTJZMFPMVõBOj2 I[ TB- CJUJWNFOFEFOJZMFEÐ[HÐOBSUBS$JTNJOIFSIBOHJCJSBO- ** R1 WF R2 ZÐLMFSJ FõJU CÐZÐLMÐLUF JTF F1 ve F2 EBLJI[ CVJLJI[OCJMFõLFTJ j EJS LVWWFUMFSJEFFõJUCÐZÐLMÐLUFEJS ++++++ *** F1 = F2 EJS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS + F 1 %Ñ[HÑOFMFLUSJLBMBOJÀJOEF + ZÑLMFSFFULJZFO ' WF V- j 2 E BZOZÌOMÑ - ZÑLMFSFFULJZFO ' JMF E [UZÌOMÑ- EÑS#VOFEFOMFR1 + R2 - ZÑLMÑEÑS'=R&JGBEF- -q TJOFHÌSFR1 =R2JTF'1 ='2EJS\"ODBLLVWWFUWFLUÌ- SFMPMEVôVJÀJO F1 = -F2 PMVS:BOU*WF** G3 E ------ %ÐõFZ EÐ[MFNEFLJ ZÐLMÐ QBSBMFM MFWIBMBS BSBTOB mR yüklü cisim jI[ZMBZBUBZGSMBUMEóOEBDJTNFFMFLU- SJLTFMLVWWFU F WF ( BóSMóFULJFUNFLUFEJS$JTNJO J[MFZFDFóJZËSÐOHF F >(JTFQBSBCPMJLI[MBOBSBL 1 ZËOÐOEFPMVS F =(JTFEPóSVTBMZËSÐOHFEFTBCJUI[MB 2 ZËOÐO- EFPMVS F <(JTFQBSBCPMJLI[MBOBSBL 3 ZËOÐOEFPMVS 55 12. *WF**
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 13 ÖRNEK 15 4ÐSUÐONFMFSJO ËOFNTFONFEJóJ EÐ[HÐO FMFLUSJL BMBOEB 4ÐSUÐONFMFSJOËOFNTFONFEJóJZFS¿FLJNTJ[PSUBNEBEÐ- BóSMóËOFNTFONFZFOR1 R2 R3QBS¿BDLMBSFMFLU- õFZEÐ[MFNMJMFWIBMBSBSBTOEB + ZÐLMÐQBS¿BDóOJ[- SJLBMBOBEJLWFZBUBZPMBSBLjI[ZMBGSMBUMEóOEBIB- MFEJóJZPMõFLJMEFLJHJCJEJS SFLFUZËOMFSJõFLJMEFLJHJCJEJS + dj A E +q B V- q1 j q2 j &LSBO q3 j 5BOFDJL\"OPLUBTOIFEFGBMQjI[ZMBGSMBUMODB# #VOBHÌSF R1 R2WFR3OFUÑSQBSÀBDLPMBCJMJS OPLUBTOB¿BSQZPS \"#NFTBGFTJOJB[BMUNBLJÀJO R1ZÑLÑOFFMFLUSJLBMBOÀFLNFLVWWFUJVZHVMBEôOBHÌSF * jI[OBSUSNB R1FMFLUSPOPMBCJMJSR3ZÑLÑOFFMFLUSJLBMBOJUNFLVWWFUJ ** ENFTBGFTJOJBSUSNB VZHVMBEôOBHÌSFR3QSPUPOPMBCJMJSR2ZÑLÑTBQNBEBO JMFSMFEJôJOFHÌSFR2ZÑLÑOÌUSPOPMBCJMJS *** 7QPUBOTJZFMGBSLOBSUSNB JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMNBMES ÖRNEK 14 1BSÀBDôOjI[BSUSMSTB QBSÀBDLMFWIBMBSBSBTOEBO \"óSMó ËOFNTFONFZFO +R ZÐLMÐ QBS¿BDL MFWIBMBSO EBIBLTBTÑSFEFÀLBS&MFLUSJLBMBOBEBIBB[NBSV[LB- UBNPSUBTOEBOBMBOBEJL j I[ZMBGSMBUMZPS1BS¿BDL QBSBCPMJLZËSÐOHFJ[MFZFSFL m ZÐLMÐMFWIBZB¿BSQZPS MS4BQNBNJLUBSB[BMS -FWIBMBSBSBTV[BLMLEZBQMQ UBOFDJLZJOFMFWIBMB- V SOUBNPSUBTOEB j I[ZMBGSMBUMZPS '=R&= q CBôOUTOBHÌSFEBSUBSTB'B[BMS d 'B[BMODB\"#NFTBGFTJB[BMS7QPUBOTJZFMJBSUODB V E = CBôOUTOBHÌSF&BSUBS'=R&EFO&BSUO- d DB 'BSUBS\"#V[BLMôBSUBS:BOU*WF**PMVS d - ÖRNEK 16 + - - ôFLJMEFLJ QBSBMFM MFWIBMBS BSBTOEB j I[ZMB GSMBUMBO + - FMFLUSPO*ZPMVOVJ[MJZPS + ------ j F- j d - V + +q +q + ++ #VOBHÌSF I + II * -FWIBMBSBSBTOEBLJFMFLUSJLBMBOOCÐZÐLMÐóÐEFóJõ- +++ NF[ &MFLUSPOVO**ZPMVOVJ[MFNFTJJÀJO ** 5BOFDJóFFULJZFOFMFLUSJLTFMLVWWFUJOCÐZÐLMÐóÐEF- * jI[ óJõNF[ ** ENFTBGFTJ *** 7QPUBOTJZFMGBSL *** 5BOFDJóJO - ZÐLMÐMFWIBZBVMBõNBTÐSFTJBSUBS OJDFMJLMFSJOEFOIBOHJMFSJUFLCBöOBB[BMUMNBMES JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS -FWIBMBS CJS ÑSFUFDF CBôM PMNBEô JÀJO E NFTBGFTJOJO &MFLUSPOVOjI[B[BMUMSTBFMFLUSPOEBIBÀPLTBQBDBô BSUNBT ZÑL NJLUBSO EFôJöUJSNF[ #V EVSVNEB FMFLUSJL JÀJOFMFLUSPO**ZPMVOVJ[MFSENFTBGFTJB[BMUMSTB BMBOÀJ[HJTBZTEFôJöNFZFDFôJJÀJOFMFLUSJLBMBOOOCÑ- ZÑLMÑôÑEFôJöNF['=R&CBôOUTOBHÌSF&EFôJöNF- V ZJODF'EFEFôJöNF[-FWIBMBSBSBTV[BLMLBSUODB UB- '=R&= q CBôOUTOBHÌSF'BSUBSWFFMFLUSPO**ZP- OFDJôJO - ZÑLMÑMFWIBZBVMBöNBTÑSFTJEFBSUBS d MVOVJ[MFS7QPUBOTJZFMGBSLOOB[BMNBT'LVWWFUJ- OJB[BMUS&MFLUSPO*EFOEBIBJMFSJEF + ZÑLMÑMFWIBZB ÀBSQBS:BOU*WF** 13. R1FMFLUSPO R2OÌUSPO R3QSPUPO 14. * **WF*** 56 15. *WF** 16. *WF**
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ÖRNEK 17 ÖRNEK 19 ôFLJMEFLJHJCJEÐ[HÐOFMFLUSJLBMBOOOCVMVOEVóVQBSB- N LÐUMFMJ ZÐLMÐ QBS¿BDL ZBMULBO JQJO VDVOEB õFLJMEFLJ MFMJLJMFWIBBSBTOBjI[ZMBHJSFONLÐUMFMJRZÐL- HJCJZÐLMÐQBSBMFMMFWIBMBSBSBTOEBEFOHFEFEJS MÐQBS¿BDLEPóSVMUVTVOVEFóJõUJSNJZPSWFFLSBOÐ[FSJO- EF0OPLUBTOB¿BSQZPS d F O T ip q j0 E m mg +- &LSBO V #VOBHÌSFQBSÀBDôOLÑUMFTJOJWFSFOCBôOUOFEJS iBÀTOBSUSNBLJÀJO 7QPUBOTJZFMGBSL NLÑUMFWF EV[BLMôOJDFMJLMFSJOBTMEFôJöUJSJMNFMJEJS 1BSÀBDôB FULJZFO ZFSÀFLJN LVWWFUJ BöBô ZÌOMÑEÑS 1BSÀBDôO TBQNBEBO HJEFCJMNFTJ JÀJO ZÑLÑ - PMVQ %FOHFöBSUOEBODJTNFFULJZFOLVWWFUMFS 'LVWWFUJZVLBSZÌOMÑPMNBMES%FOHFöBSUOEBO F qE qV '=NH R&=NH UBOi = = = mg mg mgd V qV q = mg ve m = CVMVOVS CBôOUTOB HÌSF i BÀTO BSUSNBL JÀJO 7 BSUSMNBM N B[BMUMNBM EB[BMUMNBMES d dg ÖRNEK 18 ÖRNEK 20 NLÐUMFMJZÐLMÐDJTJNZÐLMÐ,-QBSBMFMMFWIBMBSBSBTOB N LÐUMFMJ ZÐLMÐ QBS¿BDL ZBMULBO JQJO VDVOEB õFLJMEFLJ ZBMULBOCJSJQMFBTMEóOEBEÐõFZMFiB¿TZBQBDBLCJ- HJCJZÐLMÐQBSBMFMMFWIBMBSBSBTOEBEFOHFEFEJS ¿JNEFõFLJMEFLJHJCJEFOHFEFLBMZPS KdL KL T ip i m m q E +- &MFLUSJLBMBOOZÌOÑ i BÀT NLÑUMFTJ RZÑLÑWF #VOBHÌSF V HZFSÀFLJNTBCJUJCJMJOFOMFSJZMF * $JTNJOZÐLÐOÐODJOTJ * $JTNJOZÐLDJOTJQP[JUJGUJS ** &MFLUSJLTFMLVWWFU *** &MFLUSJLBMBO ** &MFLUSJLBMBO¿J[HJMFSJ,MFWIBTOEBO-ZFEPó- EFôFSMFSJOEFOIBOHJMFSJCVMVOBCJMJS SVEVS *** NLÐUMFTJBSUBSTB iB¿TB[BMS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS &MFLUSJL BMBO WFLUÌSÑ , MFWIBTOEBO - MFWIBTOB EPôSV $JTJN - ZÑLMÑMFWIBZBZBLMBöUôOBHÌSFZÑLÑ + JöB- PMEVôVOBHÌSF, + - - ZÑLMÑEÑS$JTJN,MFWIBTOB SFUMJEJS &MFLUSJL BMBO ÀJ[HJMFSJ + ZÑLMÑ , MFWIBTOEBO EPôSVBÀMEôOBHÌSFZÑLDJOTJ - EJS - ZÑLMÑ-MFWIBTOBEPôSVEVS,ÑUMFOJOBSUNBT ZFSÀF- LJNJOFLBSöBÀMNBZB[BMUS iBÀTB[BMS UBOi = F qE = :BOU* **WF*** mg mg CBôOUTOBHÌSFDJTNFFULJZFOFMFLUSJLTFMLVWWFUWFFMFLU- SJLBMBOEBCVMVOBCJMJS:BOU* **WF*** 17. N R7EpH 18. * **WF*** 57 19. 7 NE 20. * **WF***
TEST - 1 %·;(·/&-&,53÷,\"-\"/7&4*ó\" 1. ôFLJMEFLJQBSBMFMMFWIBMBSQPUBOTJZFMGBSL7PMBO 3. NLÐUMFMJZÐLMÐQBS¿BDLQBSBMFMMFWIBMBSBSBTOEB ÐSFUFDFCBóMBOBSBLZÐLMFONJõUJS õFLJMEFLJHJCJEFOHFEFEJS d øT +- m +- d +- +- +- V +- V -FWIBMBSBSBTOEBLJEV[BLMôBSUSMSTB #VOBHÌSF * -FWIBMBSOZÐLÐBSUBS * 7BSUBSTB iB[BMS ** 7QPUBOTJZFMJBSUBS ** EBSUBSTB iB[BMS *** -FWIBMBSBSBTFMFLUSJLBMBOõJEEFUJB[BMS *** NBSUBSTB iB[BMS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS ZBSHMBSOEBOIBOHJMFSJEPôSVE VS \" :BMO[* # :BMO[*** $ *WF** \" :BMO[* # :BMO[*** $ *WF** % *WF*** & * **WF*** % *WF*** & **WF*** 2. ôFLJMEFLJQBSBMFMMFWIBMBSQPUBOTJZFMGBSL7PMBO 4. ôFLJMEFLJJMFULFOWFQBSBMFMMFWIBMBSOBSBTOEBE ÐSFUFDF CBóMBOBSBL ZÐLMFOEJLUFO TPOSB ZÐL LBZC LBEBSV[BLMLWF7LBEBSQPUBOTJZFMGBSLWBSES PMNBEBOÐSFUF¿UFO¿LBSMZPS d d +- KL +- +- +- V +- #VEVSVNEB7KLQPUBOTJZFMGBSLOOBSUUSMNBT JÀJO -FWIBMBSBSBTEV[BLMôB[BMUMSTB * EV[BLMóOB[BMUNBL ** EV[BLMóOBSUUSNBL * -FWIBMBSBSBTQPUBOTJZFMGBSLB[BMS *** 7QPUBOTJZFMGBSLOBSUUSN BL ** -FWIBMBSBSBTFMFLUSJLBMBOõJEEFUJEFóJõNF[ *** -FWIBMBSOZÐLÐEFóJõNF[ JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMNBMES JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS \" :BMO[*** # *WF** $ *WF*** \" :BMO[* # :BMO[** $ :BMO[*** % **WF*** & * **WF*** % *WF*** & **WF*** 1. B 2. E 58 3. E 4. D
%·;(·/&-&,53÷,\"-\"/7&4*ó\" TEST - 2 1. :ÐLMÐ QBSBMFM JLJ MFWIB BSBTOEB õFLJMEFLJ HJCJ & 3. ¶SFUFDF CBóM QBSBMFM JLJ MFWIB BSBTOEB õFLJMEFLJ CÐZÐLMÐóÐOEFFMFLUSJLTFMBMBOPMVõVZPS HJCJ&õJEEFUJOEFFMFLUSJLTFMBMBOPMVõVZPS E d E d +- +- V #VOBHÌSFMFWIBMBSOZÑLMFSJEFôJöNFEFO * EV[BLMóOBSUSNBL #VOBHÌSF * 7HFSJMJNJOJB[BMUNBL ** -FWIBMBSBSBTOBZBMULBOLPZNBL ** EV[BLMóOBSUSNBL *** -FWIBMBSOLBSõMLMBMBOMBSOFõJUNJLUBSBSUS- *** -FWIBMBSOBMBOOBSUSNBL mak JöMFNMFSJOEFO IBOHJMFSJ UFL CBöOB ZBQMSTB & JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMSTB& EFôFSJB[BMS EFôJöNF[ \" :BMO[* # *WF** $ *WF*** \" :BMO[* # :BMO[** $ *WF** % **WF*** & * **WF*** % *WF*** & * **WF*** 2. NLÐUMFMJZÐLMÐJMFULFOLÐSF BSBMBSOEBEV[BLMó 4. 7QPUBOTJZFMGBSLJMFZÐLMFOFOQBSBMFMMFWIBMBSBSB- CVMVOBOJLJMFWIBBSBTOEBõFLJMEFLJHJCJEFOHFEFEJS TOEB Ë[EFõ ZÐLMÐ LÐSFMFS EÐõFZMF i B¿T ZBQB- DBLõFLJMEFEFOHFEFEJS d ip i i ip + ip i d m -V qq -+ V #VOBHÌSF * EB[BMSTBiEFóJõNF[ #VOBHÌSF ** 7BSUBSTB iB[BMS * ENFTBGFTJOJB[BMUNBL ** m kütlesini azaltmak *** öQCPZMBSFõJUNJLUBSB[BMSTB iBSUBS CJMHJMFSJOEFOIBOHJMFSJEPôSVEVS *** ,ÐSFOJOZÐLÐOÐB[BMUNBL JöMFNMFSJOEFO IBOHJMFSJ UFL CBöOB ZBQMSTB i \" :BMO[** # *WF** $ *WF*** BÀTB[BMS % **WF*** & * **WF*** \" :BMO[* # :BMO[** $ :BMO[*** % *WF** & **WF*** 1. \" 2. $ 59 3. $ 4. D
TEST - 3 %·;(·/&-&,53÷,\"-\"/7&4*ó\" 1. %ÐõFZEÐ[MFNEFõFLJM- 4. 4BCJU 7 QPUBOTJZFM GBSL BMUOEB ZÐLMFOFO QBSBMFM d m +q EFLJ QBSBMFM MFWIBMBS MFWIBMBS BSBTOEB CVMVOBO FóJL EÐ[MFN Ð[FSJOEFLJ NLÐUMFMJDJTJNõFLJMEFLJLPOVNEBEFOHFEFLBMZPS - V BSBTOEB +q yüklü d + +q m QBS¿BDL TFSCFTU CSB- LMEóOEBBõBóZËOEF IBSFLFUFUNFLUFEJS 1BSÀBDôOEFOHFEFLBMNBTOTBôMBNBLJÀJO * -FWIBMBSBSBT7QPUBOTJZFMGBSLBSUSMNBM ** -FWIBMBSBSBTEV[BLMóB[BMUMNBM 53° *** %FOFZ\"ZEBZBQMNBM +- JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMBCJMJS V \" :BMO[* # *WF** $ *WF*** $JTNJOZÑLÑ RPMEVôVOBHÌSF7QPUBOTJZFMGBS- LOWFS FOJGBEFBöBôEBLJMFSEFOIBOHJTJOFFöJU- % **WF*** & * **WF*** UJS TJO= DPT= HZFS¿FLJNJJWNFTJ 2. 1 BóSMóOEBLJ +q yüklü 45° CJSLÐSFDJL &CÐZÐLMÐóÐO- \" 5 mgd # 1 mgd $ 4 mgd T EFEÐ[HÐOFMFLUSJLTFMBMBO- 3q 2q 3q P EB õFLJMEFLJ HJCJ EFOHFEF % mgd & 3 mgd q 4q E +q JLFO JQUFLJ HFSJMNF LVWWFUJ EÐõFZ 5EJS ,ÑSFZFFULJFEFOFMFLUSJLTFMLVWWFU'PMEVô VOB HÌSF * T = 2 P **'=& *** T = 2 qE FöJUMJLMFSJOEFOIBOHJMFSJEPôSVEVS 5. :FS¿FLJNJOJO ËOFNTFONFEJóJ PSUBNEB E BSBMLM TJO DPT 2 /2 QBSBMFMMFWIBMBS7QPUBOTJZFMGBSLBMUOEBZÐLMFOJ- \" :BMO[* # :BMO[** $ *WF** ZPS,MFWIBTOEBOJMLI[T[CSBLMBOZÐLMÐUBOF- DJL-MFWIBTOBUTÐSFEFWBSZPS % *WF*** & * **WF*** KdL 3. %ÐõFZEÐ[MFNEF71WF72QPUBOTJZFMGBSLJMFZÐL- q MÐQBSBMFMMFWIBMBSBSBTOBCSBLMBOR1 WFR2 yüklü +- DJTJNMFSõFLJMEFLJHJCJEFOHFEFLBMZPS d m q1 + V1 2d m q2 + V2 V - - #VOBHÌSFUTÑSFTJOJOBSUNBTJÀJO * 7QPUBOTJZFMGBSLOB[BMUNB ** ENFTBGFTJOJBSUSNB $JTJNMFSJO LÑUMFMFSJ FöJU WF V1 = 2 PMEVôVOB *** m kütlesini azaltma q1 V2 3 JöMFNMFSJOEFOIBOHJMFSJZBQMNBMES q2 HÌSF PSBOLBÀUS \" :BMO[* # *WF** $ *WF*** \" 2 # 3 $ % 3 & 9 % **WF*** & * **WF*** 3 4 24 1. E 2. D 3. B 60 4. $ 5. B
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF :ÑLMÑ1BSBMFM-FWIBMBS %m/*m 1BSBMFMMFWIBMBS CJSQJMZBS- 1BSBMFM MFWIBMBS BSBTOB LPOVMBO ZÐLMÐ QBS¿BDóB EN JMF ZÐLMFOEJLMFSJOEF FULJFEFOLVWWFU QBS¿BDLÐ[FSJOEFJõZBQBSBLQBS- d MFWIBMBS BSBTOEB EBO ¿BDóOFOFSKJTJOJEFóJõUJSFCJMJS E m ZF EPóSV EÐ[HÐO CJS 8 'Y Ó& FMFLUSJLBMBOPMVõVS F yerine qV yazarsak +- #V FMFLUSJL BMBOO CÐZÐL- MÐóÐ d V W = qV . x E=V d d QBS¿BDLMFWIBMBSOCJSVDVOEBOEJóFSVDVOBHJEFS- E:FMFLUSJLBMBOõJEEFUJ TFY EPMBDBóJ¿JO 71PUBOTJZFMGBSL W = qV . d R7 d EMFWIBMBSBSBTOEBLJNFTBGF õFLMJOEFCVMVOVS õFLMJOEFCVMVOVS &MFLUSJL BMBOO J¿JOF ZÐLMÐ CJS QBS¿BDL LPOVMEV- W::BQMBOJõ óVOEB QBS¿BDóB FMFLUSJLTFM LVWWFU FULJ FEFS #V LVWWFU FMFLUSJLBMBOBQBSBMFMPMBDBLõFLJMEF QP[JUJG '1BS¿BDóBFULJFEFOFMFLUSJLTFMLVWWFU ZÐLMÐ QBS¿BDL J¿JO FMFLUSJL BMBOMB BZO ZËOEF OF- HBUJGZÐLMÐQBS¿BDLJ¿JOJTFFMFLUSJLBMBOMBUFSTZËO- Ô&1BS¿BDóOFOFSKJEFóJõJNJ EFPMVõVS,VWWFUJOCÐZÐLMÐóÐJTF x:1BS¿BDóOFMFLUSJLBMBOBQBSBMFMPMBSBLBMEóZPM ' R& qV d d ' R& qV d +q x 8 'Y qV . x d F E & V F dq +- ',VWWFUJOCÐZÐLMÐóÐ V R1BS¿BDóOZÐLÐ E:&MFLUSJLBMBOõJEEFUJ 1BS¿BDóBTBEFDFFMFLUSJLTFMLVWWFUJOFULJFUUJóJEV- 71PUBOTJZFMGBSL SVNJ¿JOQBS¿BDóOJWNFTJJTF E-FWIBMBSBSBTOEBLJNFTBGF PMBSBLCVMVOVS d ' qV NB d d B qV +q –q dm F F E E õFLMJOEFCVMVOVS B1BS¿BDóOJWNFTJ +- +- '1BS¿BDóBFULJFEFOLVWWFU 71PUBOTJZFMGBSL VV E-FWIBMBSBSBTNFTBGF N1BS¿BDóOLÐUMFTJ 61
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr )[MBOESDWF4BQUSD-FWIBMBS ÖRNEK 21 d1 , :FS¿FLJNJWFTÐSUÐONFMFSJOËOFNTFONFEJóJCJSPSUBNEB +q j0 + VS d2 EÐõFZEÐ[MFNEF.OPLUBTOEBOTFSCFTUCSBLMBODJTJN m 7HQPUBOTJZFMGBSLBMUOEBI[MBOZPSWFZBUBZMFWIBMBS - BSBTOEB7SQPUBOTJZFMGBSLBMUOEBILBEBSTBQZPS h d1 VS , +- +q d2 M h m VH )[MBOESDMFWIBMBSDJTNFI[LB[BOESS +- R7H 1 m j 2 VH 2 0 , #VOBHÌSF 1BS¿BDL,ZPMVOVUTÐSFEFBMSTB t = * 7HWF7SQPUBOTJZFMMFSJCJSMJLUFJLJLBUBSUBSTBIEF- 4BQNBNJLUBSI 1 at2JMFCVMVOVS j0 2 óJõNF[ 1BS¿BDóOTBQUSDEBLJJWNFTJB q·Vs PMVS ** E1B[BMSTBIBSUBS *** E2JLJLBUBSUBSTB ITBQNBNJLUBSEBJLJLBUBSUBS d2·m JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS I 1 · qVS ·f , 2 2 d2m j0 p CVMVOBOCVJGBEFEF j20 = 2qVH 4BQNBNJLUBS m ZFSJOFZB[MSTB 1 V ,2 h= S 4 d VH h = 1 · qVS · ,2m 2 2 d2m 2qVH CBôOUTOBHÌSF7HWF74QPUBOTJZFMMFSJFöJUNJLUBS V 1 VS ,2 ·· S BSUBDBôJÀJO PSBOBZOLBMS IEFôJöNF[ V H ITBQNBNJLUBSE1V[BLMôOBCBôMEFôJMEJSE2V[BL- h= CVMVOVS MôJLJLBUBSUBSTBILBUB[BMS:BOU* 4 d2 VH ÖRNEK 22 L M K d 2d .qk(7$k, mj 2j d1V[BLMóIFULJMFNF[ +q $JTNJOLÐUMFTJWFZÐLÐIFULJMFNF[ + - -+ q PSBOIFULJMFNF[ 3V V m :FSÀFLJNJWFTÑSUÑONFMFSJOÌOFNTFONFEJôJQBSBMFM VS PSBOEFóJõNFZFDFLõFLMJEF7SWF7H MFWIBMBSOJÀJOF,EFOjI[ZMBHJSFONLÑUMFMJZÑLMÑ VH UBOFDJL-MFWIBTOjI[ZMBHFÀUJôJOFHÌSF .MFW- IBTOBLBÀjI[ZMBÀBSQBS OJOBSUNBTZBEBB[BMNBTIFULJMFNF[ 62 21. :BMO[* 22. 3
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ,-MFWIBMBSBSBTOEBFOFSKJLPSVNVOEBO ÖRNEK 24 1 mj2 + q3V = 1 m (2j) 2 22 NLÐUMFMJWFmRZÐLMÐQBS¿BDL ZÐLMÐQBSBMFMJMFULFOMFW- IBMBSOBSBTOBLPOVMVODBEÐõFZEÐ[MFNEFõFLJMEFLJHJ- q3V = 1 m3j2 CJEFOHFEFLBMZPS 2 F1 2m + V qV = 1 mj2 d -q m +q 2 - mg 2mg CVMVOVS F2 -.MFWIBMBSBSBTOEBFOFSKJLPSVNVOEBO #VOB HÌSF MFWIBMBS BSBTOB WF BZO OPLUBZB N 1 m (2j2 ) - qV = 1 m (j›) 2 LÑUMFMJWF+RZÑLMÑQBSÀBDLLPOVMVSTB QBSÀBDôO 22 JWNFTJLBÀHPMVS HZFS¿FLJNJJWNFTJ 1 m4j2 - 1 mj2 = 1 m (j›) 2 2 22 j› = 3j ÖRNEK 23 -RZÑLÑEFOHFEFPMEVôVOBHÌSF :ÐLMÐQBSBMFMMFWIBMBSBSBTOEB,MFWIBTOEBOTFSCFTU '1 =NHÁ q V = mg bulunur. CSBLMBONLÐUMFMJ+RZÐLMÐUBOFDJL-OPLUBTOEBOj d I[JMFHF¿JQ.OPLUBTOBjMI[JMF¿BSQZPS +RZÑLÑJÀJO NH+'2 ddd 2mg + qV ( 2mg + mg = 3mg bulunur. d LM '=NBJGBEFTJOEFO j jM K 3mg = ma B=HCVMVOVS +- ÖRNEK 25 V 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFCVMVOBOZÐLMÐQBSBMFMMFW- IBMBS BSBTOEBLJ , OPLUBTOEBO & LJOFUJL FOFSKJTJ JMF #VOBHÌSF jMI[LBÀjEJS GSMBUMBO+RZÐLMÐDJTJN-OPLUBTOEBOHFSJEËOÐZPS :FS¿FLJNJJWNFTJJINBMFEJMJZPS 3d d ,WF-OPLUBMBSBSBTOEBFOFSKJLPSVNVOEBO +q E K qV = qV + 1 mj2 L 32 m 2qV = 1 mj2 CVMVOVS 32 ,WF.OPLUBMBSBSBTOEBFOFSKJLPSVNVOEBO -+ qV = 1 m `jMj2 CVMVOVS V 2 #VOBHÌSFDJTNJOLJOFUJLFOFSKJTJ&LBÀRp7EJS ÷LJ EFOLMFNJO PSUBL ÀÌ[ÑNÑOEFO j = 3 j CV- :FS¿FLJNJËOFNTFONJZPS M2 MVOVS ,WF-OPLUBMBSBSBTOEBFOFSKJLPSVOVNVOEBO E +R -7 = q d- V n 4 qV E =R7- 4 3qV E = CVMVOVS 4 3 63 24. 3 25. 3 23. 4 2
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 26 ÖRNEK 28 %ÐõFZ EÐ[MFNEF õFLJMEFLJ HJCJ ZÐLMÐ QBSBMFM MFWIBMBSO :BUBZ EÐ[MFNEF ZÐLMÐ QBSBMFM MFWIBMBS JMF IB[SMBOBO ,OPLUBTOEBOTFSCFTUCSBLMBO+RZÐLMÐQBS¿BDL- ôFLJM-I EFLJ EÐ[FOFóF , MFWIBTOEBO j I[ZMB HJ- OPLUBTOEBO&LJOFUJLFOFSKJTJJMFHF¿JZPS SFO ZÐLMÐ UBOFDJóF BJU I[m[BNBO HSBGJóJ ôFLJM-II deki HJCJPMVZPS d 2d KL M K L M )[ d1 d2 3j j 3j 2j 2j +- -+ 2V V -+ +- j #VOBHÌSFQBSÀBDôO.OPLUBTOBÀBSQNBLJOFUJL V1 V2 0 t 2t ;BNBO FOFSKJTJLBÀ&PMVS :FS¿FLJNJËOFNTFONJZPS ôFLJMmI ôFLJMmII ,WF-OPLUBMBSBSBTOEBFOFSKJLPSVOVNVOEBO q . 2V = 1 mj2 #VOB HÌSF ,- BSBTOEBLJ V[BLML E1 QPUBOTJZFM 2L GBSL71WF-.BSBTOEBLJV[BLMLE2WFQPUBOTJZFM Rp7=&CVMVOVS -WF.OPLUBMBSBSBTOEBFOFSKJLPSVNVOEBO GBSL72PMEVôVOBHÌSF d1 ile V1 PSBOMBSLBÀUS d2 V2 E +R -7 = 1 mj2 ÁR7-R7= EM 2M R7= EM Á EM = E CVMVOVS 2 ,WF-BSBTOEBDJTJNÑ[FSJOFZBQMBOI[MBOESDJö ÖRNEK 27 1 mj2 + q V = 1 m (3j) 2 2 11 2 KL M qV = 1 m8j2 d 4d 12 -WF.BSBTOEBLJZBWBöMBUDJö 1 m (3j) 2 - qV = 1 m (2j) 2 2 22 qV = 1 m5j2 22 CBôOUMBSPSUBLÀÌ[ÑMÑODF +- -+ V 8 1 = V1 = 2V V2 = 5V V5 2 4ÑSUÑONFTJ[ZBUBZEÑ[MFNEFCVMVOBOöFLJMEFLJZÑL- PMVS MÑ , - WF . MFWIBMBSOEBO , OO ÌOÑOEFO TFS- CFTUCSBLMBO+RZÑLMÑDJTJN.MFWIBTOBLBÀE )[m[BNBOHSBGJôJOJOBMBOHJEJMFOZPMVWFSJS ZBLMBöBCJMJS (j + 3j) t ,- MFWIBMBS BSBTOEB DJTJN Ñ[FSJOF ZBQMBO I[MBOE- d= SDJö -.MFWIBMBSBSBTOEBLJZBWBöMBUDJöFFöJUUJS 12 = 2jt W=W (3j + 2j) t d= R71 ='pY R71 =R&pY 22 = 5 jt 2 V d = 4 bulunur. qV = q 2 · x 1 1d d5 2 V 2V 2 x= 1 ·d %VSNBNFTBGFTJ x = · 4d V2 5V 2 x = EPMVQ.MFWIBTOB EZBLMBöBCJMJS 26. 1 27. 2,4 64 28. d = 4 V = 8 2 1 1 d 5V 5 22
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11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr %Ñ[MFN,POEBOTBUÌS %m/*m TANIM 4óBT$PMBOCPõCJSLPO- EBOTBUËS7HFSJMJNMJÐSFUF- C DF CBóMBOQ BOBIUBS LB- QBUMEóOEB ZÐL IBSFLFUJ Armatür CBõMBS #V TSBEB BNQFS- JMFULFOMFWIB metrede sürekli azalan bir BLNHË[MFOJS :BMULBONBEEF A +– ¶SFUFDJO QPUBOTJZFMJOF WF ôFLJMEFLJ EÐ[MFN LPOEBOTBUËS CJS ÐSFUFDF CBóMBO- LPOEBOTBUËSÐO TóBTOB C CBóM R 7$ LBEBS ZÐL EóOEB q = C eõJUMJóJOFHËSFZÐLLB[BOS LPOEBOTBUËSF EFQPMBOE- V ++ –– óOEB ZÐL IBSFLFUJ TPOB ++ –– FSFS \"NQFSNFUSF CV BO- %Ð[MFN LPnEBOTBUËSÐO TóBT C = f A GPSNÐ- EBO JUJCBSFO TGS EFóFSJOJ d +q –q HËTUFSJS MÐOEFOIFTBQMBOS A +– V \" 1BSBMFMMFWIBMBSOBMBO N2 -FWIBMBSUBNLBSõ LBSõZBEFóJMTF¿BLõBOLTNMBSOBMBOBMOS E -FWIBMBSBSBTV[BLML N .qk(7$k, #JSLPOEBOTBUËSÐOZÐLÐEFOJMEJóJOEFJõBSFUJOF f: %JFMFLUSJL TBCJUJ ZB EB ZBMULBOML TBCJUJ c F m CBLMNBLT[O UFL CJS MFWIBTOEB EFQPMBONõ ZÐLNJLUBSBMOS m .BEEFMFSJO DJOTJOF HËSF ZBMULBOMLMBS EFóJõJS 7BLVNPSUBNOO CPõMVóVO EJFMFLUSJLTBCJUJ f0 = 8, 854x10–12 F EJS :BMULBOO DJOTJOF ,POEBOTBUÌSÑO,VMMBON\"MBOMBS m %m/*m HËSFEJFMFLUSJLTBCJUJfr dir ,POVOVOCBõOEBTPSEVóVNV[TPSVMBSODFWBQMBSO f f · f B¿LMBZBMN r 'PUPóSBGNBLJOFTJOJOúBõOBTM¿BMõS ¶SFUFDFCBóMZÐLMÐCJSLPOEBOTBUËSÐOMFWIBMBSBSB- GPSNÐMÐOEFOZBMULBONBEEFMFSJOCPõMVóBHËSFCB- TOBJMFULFOCBóMBOQ LTBEFWSF EFQPMBOBOZÐLÐO FOFSKJOJO BOJEFO CPõBMNBT TBóMBOS #V TSBEB L- óM EJFMFLUSJL LBUTBZMBS IFTBQMBOS :BMULBOML BSU- WMDN PMVõVS ,POEBOTBUËSF EFQPMBOBO ZÐL ZB EB FOFSKJ OF LBEBS GB[MB JTF P LBEBS QBSMBL CJS LWMDN UL¿BTóBBSUBS FMEFFEJMJS'PUPóSBGNBLJOFTJOJOúBõOO PUPNPCJMMFS- EFLJBUFõMFNFTJTUFNJOJO FMFLUSPõPLBMFUJOJO¿BMõNB :ÐL DPVMPNC #JS LPOEBOTBUËSÐO T- NBOUóCVEVS#VBZO[BNBOEBZBQBZZMESNES q óBTTBCJULBMNBLõBS- UZMB ZÐLÐOÐO HFSJMJNF &MFLUSPOJL BMFUMFS LBQBUMEó IBMEF Ð[FSMFSJOEF CVMV- a HËSF EFóJõJN HSBùóJ OBO CB[ õLMBS LTB TÐSFMJóJOF EF PMTB OFEFO ZBO- V (FSJMJN WPMU õFLJMEFLJHJCJEJS NBZBEFWBNFEFS %PóSV BLN LBZOBóOB CBóM CPõ CJS LPOEBOTBUËS m (SBùóJOFóJNJTóBZWFSJS LTBTÐSFEFEPMBSWFMFWIBMBSBSBTOEBCJSQPUBOTJZFM GBSL PMVõVS ¶SFUF¿ EFWSFEFO BZSMEóOEB LPOEBO- tana = q =C (Farad) TBUËSLFOEJOFQBSBMFMCBóMMBNCBÐ[FSJOEFOZÐLÐOÐ V CPõBMUNBZBCBõMBS#VEVSVNLTBTÐSFMJóJOFEFPMTB EFWSFZF BLN TBóMBS ,BQBUMBO FMFLUSPOJL BMFUMFSJO m ( SBùóJOBMBOLPOEBOTBUËSEFEFQPMBOBOFOFSKJZJ LTBTÐSFMJóJOFEFPMTBCB[õLMBSOOZBONBZBEF- WFSJS WBNFUNFTJ LBQBUMBOCJSIPQBSMËSEFOCFMJSMJCJSTÐSF TFTHFMNFZFEFWBNFUNFTJ QJMJ¿LBSMBOCJSDFQUF- qV = 1 CV2 = q2 = E (Joule) MFGPOVOVO LTB TÐSF J¿JOEF UFLSBS UBLMEóOEB TBBU 22 2C BZBSJTUFNFNFTJCVEVSVNBËSOFLHËTUFSJMFCJMJS 68
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11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 32 ÖRNEK 34 :BQSBLMBS,WF-PMBOCPõCJSLPOEBOTBUËSÐSFUFDFõF- , LPOEBOTBUËSÐOÐO MFWIBMBSOO IFSCJSJOJO ZÐ[FZ BMBO LJMEFLJHJCJCBóMBONõUS \" MFWIBMBS BSBT V[BLML E BSBMBSOEBLJ ZBMULBO NBE- KL denin dielektrik sabiti fEJS-LPOEBOTBUËSÐOÐOMFWIBMB- S SOOIFSCJSJOJOZÐ[FZBMBO A MFWIBMBSBSBTV[BLMLE V 2 4 BOBIUBS LBQBUMEôOEB PL ZÌOÑOEF BLN HFÀUJôJ- BSBMBSOEBLJZBMULBONBEEFOJOEJFMFLUSJLTBCJUJfEJS OFHÌSF * ,ZBQSBóOFHBUJGZÐLMFONJõUJS 2d d ** #JSTÐSFTPOSBLPOEBOTBUËSHFSJMJNJ7PMVS *** #JSTÐSFTPOSBEFWSFEFOBLNHF¿NF[ A fA A ZBSHMBSOEBOIBOHJMFSJEPôSVEVS 2 4f #BöMBOHÀUB CPö PMBO LPOEBOTBUÌS ÑSFUFDF CBôMBOO- DB EPMNBZB CBöMBS \"LN FMFLUSPO IBSFLFUJOF [U ZÌOEF KL PMBDBô JÀJO HÌTUFSJMFO ZÌOEF BLN HFÀFS ,POEBOTBUÌ- SÑO HFSJMJNJ ÑSFUFÀ HFSJMJNJOF FöJU PMBOB LBEBS ZÑL HFÀJ- #VOB HÌSF , WF - LPOEBOTBUÌSMFSJOJO TôBMBS PSBO öJ PMVS ,POEBOTBUÌS EPôSV BLN EFWSFTJOF CBôMBOEôO- CK LBÀUS EB EPMBOB LBEBS Ñ[FSJOEFO BLN HFÀFS EPMEVLUBO TPOSB CL BLNHFÀNF[ :BOU* **WF*** C = f A CBôOUTOBHÌSF d CK = f·A 1 bulunur. C = 2 =1 2d L 24 4f· A 2 d ÖRNEK 33 ÖRNEK 35 4óBT$PMBOCJSEÐ[MFNLPOEBOTBUËSÐOMFWIBMBSOOZÐ- r #JMHJTBZBSLMBWZFTJ [FZBMBOJLJLBUOB¿LBSMQMFWIBMBSOBSBTOEBLJV[BL- r )PQBSMËSEFTFTLBZCOËOMFNF MLZBSZBJOEJSJMJZPS r 'PUPóSBGNBLJOBTOOGMBõ 4POEVSVNEBLPOEBOTBUÌSÑOTôBTLBÀ$PMVS r &MFLUSPõPLBMFUMFSJ r $FQUFMFGPOVOEBCJMHJLBZCOËOMFNF C = f A CBôOUTOBHÌSF\"LBUBSUBSTB$LBUBSUBS :VLBSEBLJMFSEFOLBÀUBOFTJTôBDOHÑOMÑLIBZBUUB- LJLVMMBONBMBOMBSOEBOES d EJLJLBUB[BMSTB$JLJLBUBSUBS4POVÀUB$LBUBSUBS :VLBSEBLJÌSOFLMFSJOUBNBNLPOEBOTBUÌSÑOHÑOMÑLIB- ZBUUBLJLVMMBONBMBOMBSOEBOES 32. * **WF*** 33. 4 70 34. 1 35. 5 4
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ÖRNEK 36 ÖRNEK 39 #JSQJMFCBôMBOQ2ZÑLÑJMFZÑLMFONJöCJSTôBÀQJM- ôFLJMEFLJTóB¿7QPUBOTJZFMGBSLBMUOEBZÐLMFONJõPMVQ EFO BZSMELUBO TPOSB QMBLBMBS BSBT V[BLML BSUUSM- ZÐLMFSJOJLBZCFUNFEFOÐSFUF¿UFOBZSMNõUS#VEVSVN- EôOEBEFQPMBEôFOFSKJOJOOBTMEFôJöUJôJOJGJ[JLTFM EBMFWIBMBSBSBTOBZBMULBONBEEFLPOVMVZPS CJSCBLöBÀTJMFBÀLMBZO[ f ÷LJQMBLBFöJUWF[UZÑLMFZÑLMFOJS#JSCJSJOEFOV[BLMBöUSM- EôOEBJöZBQMS QPUBOTJZFMFOFSKJBSUBS ÖRNEK 37 #VOBHÌSF TôBDOTôBT$ MFWIBMBSBSBTQPUBOTJ- ZFMGBSL7 MFWIBMBSBSBTFMFLUSJLBMBO&WFZÑLÑ2 #JSTôBDOTôBTOBSUUSNBLJÀJOMFWIBBMBOMBS\" OJDFMJLMFSJOEFOIBOHJMFSJB[BMS MFWIBMBSBSBTOEBLJV[BLMLEWFMFWIBMBSBSBTOEBLJ C = f A CBôOUTOBHÌSFfBSUBSTB$BSUBS,POEBO- PSUBNOEJFMFLUSJLTBCJUJfOBTMEFôJöUJSJMNFMJEJS d C = f A CBôOUTOBHÌSF \"WFfBSUSMNBM EB[BM- TBUÌSÑSFUFÀUFOBZSMODB2TBCJUPMVS d 2=$p7JGBEFTJOEF$BSUODB7B[BMS UMNBMES E = V JGBEFTJOFHÌSF7B[BMODB&B[BMS d :BOU7WF& ÖRNEK 40 ôFLJM-I EFLJ LPOEBOTBUËS 7 HFSJMJNJ BMUOEB 2 ZÐLÐOÐ EFQPFEFSLFO MFWIBMBSBSBTOEBLJFMFLUSJLBMBO&PMVZPS ÖRNEK 38 +– +– 1BSBMFMQMBLBMTóB¿ CJSQJMFCBóMBOQZÐLMFOEJLUFOTPO- V V SBQJMJMFPMBOCBóMBOUTLFTJMNJõUJS 1BSBMFM QMBLBMBS BSBT V[BLML JLJ LBUOB ÀLBSMEôO- ôFLJMI ôFLJMII EB TôBÀUBEFQPMBOBOFOFSKJOBTMEFôJöJS -FWIBMBS BSBTOB õFLJM-II EFLJ HJCJ ZBMULBO LPOVM- 4ôBÀZÑLMFOEJLUFOTPOSBQJMEFOBZSMSTBZÑLÑTBCJULBMS EVôVOEB7 2WF&EFôFSMFSJOBTMEFôJöJS C = f A JGBEFTJOFHÌSFEJLJLBUBSUBSTB$JLJLBUB[BMS C=f A CBôOUTOBHÌSFfBSUODB$BSUBS,POEBO- d d 4ôBÀQJMEFOBZSMODBZÑLÑTBCJULBMS TBUÌSÑSFUFDFCBôMZLFO7TBCJUUJS 2=$p7JGBEFTJOEF$JLJLBUB[BMODB7JLJLBUBSUBS 2=$p7EFO$BSUBSTB2BSUBS W = 1 C V2 JGBEFTJOFHÌSF8JLJLBUBSUBS 2 E= V PMEVôVOBHÌSF7TBCJULFO&EFôJöNF[ d 36. ÷LJQMBLBFöJUWF[UZÑLMFZÑLMFOJS#JSCJSJOEFOV[BLMBöUSM- 39. 7WF& 40. 7WF&EFôJöNF[ 2BSUBS EôOEBJöZBQMS QPUBOTJZFMFOFSKJBSUBS 1. ? 2. ? 71 37. \"WFfBSUSMNBM EB[BMUMNBMES 38. ÷LJLBUBSUBS
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 41 ÖRNEK 43 #JS LPOEBOTBUËSÐO ZÐLÐOÐO QPUBOTJZFMMF EFóJõJN HSBGJ- ¶SFUF¿ LPOEBOTBUËS BOBIUBSWFMBNCBEBOPMVõBOEPó- óJõFLJMEFLJHJCJEJS SVBLNEFWSFTJõFLJMEFLJHJCJEJS :ÐL I II III 1PUBOTJZFM +– #VOBHÌSFCVLPOEBOTBUÌSÑOTôBTI, IIWFIII #VOBHÌSF BOBIUBSLBQBUMEôOEBMBNCBOOQBSMBL- BSBMLMBSOEBOBTMEFôJöNJöUJS MôOBTMEFôJöJS ,POEBOTBUÌS EPôSV BLNB CBôMBOEôOEB EPMBOB LBEBS Ñ[FSJOEFOBLNHFÀFS-FWIBMBSOQPUBOTJZFMJÑSFUFDJOQP- UBOTJZFMJOF FöJUMFOJODF EFWSF BLN LFTJMJS #V EVSVNEB MBNCBOOQBSMBLMôTÑSFLMJB[BMSWFCJSTÑSFTPOSBTÌOFS ICÌMHFEF C = Q CBôOUTOEBHÌSFFôJNBZOLBMEô- V OBHÌSF$EFôJöNF[IICÌMHFEF7EFLJBSUö2EBOEB- IBGB[MBES$B[BMSIIICÌMHFEFZÑLTBCJULFO7BSUBS- TB$B[BMS :BOU%FôJöNF[ \"[BMS \"[BMS ÖRNEK 42 ÖRNEK 44 -FWIBMBSBSBTOEBLJV[BLMLELBEBSPMBOõFLJMEFLJLPO- ôFLJMEFLJEFWSFEF,WF-LPOEBOTBUËSMFSJË[EFõUJS- EBOTBUËS7QPUBOTJZFMGBSLBMUOEBZÐLMFOJZPS OJOMFWIBMBSBSBTOBZBMULBONBM[FNFLPOVMVZPS d f KL +– +– V V #BöLBCJSEFôJöJLMJLZBQNBEBOEV[BLMôB[BMUMSTB #VOBHÌSF-LPOEBOTBUÌSÑOÑOTôBT ZÑLÑWFMFW- * ,POEBOTBUËSÐOTóBT $ IBMBSBSBTOEBLJQPUBOTJZFMGBSLOBTMEFôJöJS ** ,POEBOTBUËSÐOZÐLÐ R *** -FWIBMBSOBSBTOEBLJFMFLUSJLTFMBMBO & C=f A CBôOUTOEBHÌSFfBSUBSTB$BSUBS$OJO d OJDFMJLMFSJOEFOIBOHJMFSJBSUBS BSUNBTÑ[FSJOEFLJQPUBOTJZFMGBSLB[BMUS4ôBDOBSUNB- C = f A CBôOUTOEBEB[BMSTB$BSUBS TZÑLÑOÑEFBSUSS d 2=$p7EFLPOEBOTBUÌSÑSFUFDFCBôMZLFO7TBCJUUJS :BOU\"SUBS \"SUBS \"[BMS $BSUODB2BSUBS E = V JGBEFTJOEF7TBCJULFOEB[BMSTB&BSUBS d :BOU* **WF*** 41. %FôJöNF[ \"[BMS \"[BMS 42. * **WF*** 72 43. \"[BMSWFTÌOFS 44. \"SUBS \"SUBS \"[BMS
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ÖRNEK 45 ÖRNEK 47 4óBMBS$ $WF$PMBOLPOEBOTBUËSMFSJOTFSJCBó- 4óBMBS$PMBOË[EFõ, -WF.LPOEBOTBUËSMFSJõF- MBONBTJMFõFLJMEFLJEFWSFPMVõUVSVMVZPS LJMMFSEFLJHJCJCBóMBONõMBSES C 2C 3C CK K LM CCC CL +– KL M CM V +– V +– #VOBHÌSF , - .LPOEBOTBUÌSMFSJOJOZÑLMFSJRK , V RL RMWFQPUBOTJZFMGBSLMBS7K 7L 7MBSBTO- ôFLJMmI EBLJCÑZÑLMÑLTSBMBNBTOFEJS ôFLJMmII 4FSJCBôMEFWSFMFSEFZÑLBZOES#VEVSVNEBRK =RL =RM %Ñ[FOFL õFLJM-I EFO õFLJM-II EFLJ EVSVNB HFUJSJM- PMVS2=$p7JGBEFTJOFHÌSF2TBCJULFO$BSUBSTB 7 EJôJOEF , LPOEBOTBUÌSÑOÑO ZÑLÑ QPUBOTJZFMJ WF B[BMS FOFSKJTJOBTMEFôJöJS 7K >7L >7MPMVS 4FSJ CBôMBNBEB ZÑL QBSBMFM CBôMBNBEB HFSJMJN BZOES ,OOJMLQPUBOTJZFMJ V JLFOQBSBMFMCBôMBOODB7PMVS 3 4ôBTJTFEFôJöNF[R=$7CBôOUTOEBO$TBCJULFO 7BSUBSTB REBBSUBS W = 1 C·V2 JGBEFTJOFHÌSF7BSUBSTB8EBBSUBS 2 ÖRNEK 46 ÖRNEK 48 4óBMBS $ $ WF $ PMBO LPOEBOTBUËSMFSJO QBSBMFM ôFLJMEF TBCJU HFSJMJN BMUOEB ZÐLMFOFO LPOEBOTBUËS WF- CBóMBONBTJMFõFLJMEFLJEFWSFPMVõUVSVMVZPS SJMJZPS C KC q L 2C +– M 3C V +– V #VLPOEBOTBUÌSFBJUIBOHJHSBGJLMFSEPôSVEVS #VOBHÌSF, - .LPOEBOTBUÌSMFSJOJOZÑLMFSJRK , $ TóB 2 ZÐL $ TóB RL RMWFQPUBOTJZFMGBSLMBS7K 7L 7MBSBTO- EBLJCÑZÑLMÑLTSBMBNBTOFEJS V V V (FSJMJN (FSJMJN (FSJMJN 2=$p7JGBEFTJOFHÌSF7TBCJULFO$BSUBSTB 2BSUBS #VEVSVNEBRM >RL >RKPMVS I II III 1BSBMFMCBôMEFWSFMFSEFQPUBOTJZFMGBSLBZOES 7K =7L =7MEJS C = f A PMVQ7OJOBSUNBT$ZJEFôJöUJSNF[2=$p7 d CBôOUTOEB R WF 7 OJO CJSMJLUF EÑ[HÑO BSUNBT EVSV- NVOEB$TBCJULBMS :BOU*WF** 45. RK RL RM 7K 7L 7M 46. RM RL RK7K 7L 7M 73 47. )FQTJBSUBS 48. *WF**
TEST - 4 4*ó\" 1. 4ôBWFLPOEBOTBUÌSMFSJMFJMHJMJ 3. 4óBT$ MFWIBMBSBSBTQPUBOTJZFMGBSL7PMBOCJS * 4óBOOCJSJNJ'BSBEES LPOEBOTBUËSÐOZÐLÐRLBEBSES ** ,POEBOTBUËSÐOV¿MBSBSBTOEBZÐLQPUBOTJZFM ,POEBOTBUÌSÑO ZBMO[ MFWIBMBS BSBTOEBLJ QP- PSBOTBCJUUJS UBOTJZFM GBSL ZBSZB EÑöÑSÑMÑSTF LPOEBOTBUÌ- *** ,POEBOTBUËSJLJJMFULFOJOBSBTOBZFSMFõUJSJMNJõ SÑOZÑLÑWFTôBTOOEFôJöJNJJÀJOOFTÌZMFOF- CJMJS ZBMULBOPSUBNMBSEBOPMVõVS :ÑL R 4ôB $ JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS \" \"[BMS \"SUBS # \"SUBS %FóJõNF[ \" :BMO[* # *WF** $ *WF*** $ \"[BMS %FóJõNF[ % \"[BMS \"[BMS % **WF*** & * **WF*** & %FóJõNF[ \"[BMS 2. 4óBT$PMBOCJSEÐ[MFNLPOEBOTBUËS7QPUBOTJ- 4. #JS EÑ[MFN LPOEBOTBUÌSÑO TôBTO $ BSUS- ZFMGBSLBMUOEBôFLJM-IEFLJHJCJZÐLMFOEJLUFOTPO- NBLJÀJO SBZÐLÐLPSVOBSBLÐSFUF¿UFOBZSMQôFLJM-II deki * -FWIBMBSBSBTOEBLJEJFMFLUSJLTBCJUJOJBSUSNBL LPOVNBHFUJSJMJZPS ** -FWIBMBSOZÐ[FZBMBOOBSUSNBL *** -FWIBMBSBSBTV[BLMóB[BMUNBL C JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMBCJMJS \" :BMO[* # *WF** $ *WF*** ZBMULBO % **WF*** & * **WF*** +– +– 5. #JS LPOEBOTBUËSF BJU ZÐL-HFSJMJN HSBGJóJ õFLJMEFLJ ôFLJMmII V HJCJEJS ôFLJMmI :ÐL õFLJM-II EF LPOEBOTBUÌSÑO MFWIBMBS BSBTOB a ZBMULBO NBEEF LPOVMBSBL EJFMFLUSJL LBUTBZT (FSJMJN f BSUSMSTB #VOB HÌSF HSBGJôJO FôJNJ UBO a EFôFSJ OFZJ WFSJS * ,POEBOTBUËSÐOTóBTB[BMS ** ,POEBOTBUËSÐOZÐLÐB[BMS *** -FWIBMBSBSBTOEBLJQPUBOTJZFMGBSLB[BMS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[*** $ *WF** \" -FWIBMBSOBMBO # %JFMFLUSJLLBUTBZ % *WF*** & * **WF*** $ ,BQBTJUF % &MFLUSJLBMBO & &OFSKJ 1. E 2. B 74 3. $ 4. E 5. $
4*ó\" TEST - 5 1. * &MFLUSPOJLEFWSFMFSEFQBSB[JUTJOZBMMFSJFOHFM- 4. ôFLJMEFLJ HSBGJL CJS TóBDB BJU ZÐL-QPUBOTJZFM GBSL MFNFLJ¿JOTóB¿LVMMBON HSBGJóJEJS ** %PLUPSMBSO CÐZÐL TóBM FMFLUSPõPL DJIB[MBS :ÐL LVMMBONBT q *** 5FTJTBU¿MBSO EVWBS J¿JOEF NFUBM CPSVMBS CVM- NBLJ¿JOTóB¿MEFEFLUËSLVMMBONBT :VLBSEBLJ ÌSOFLMFSEFO IBOHJMFSJ TôBÀMBSO HÑOMÑL ZBöBNEBLJ VZHVMBNB BMBOMBSOB ÌSOFL PMBSBLWFSJMFCJMJS \" * **WF*** # **WF*** $ *WF*** 0 1PUBOTJZFM'BSL V % *WF** & :BMO[** RWF7EFôFSMFSJCJMJOEJôJOFHÌSF * 4óBDOMFWIBMBSOOBMBOMBS 2. %Ñ[MFNQMBLBMLPOEBOTBUÌSMFSJOTôBTJMFJMHJMJ ** 4óBDOTóBT * :BMO[CJSQMBLBOOBMBOBSUSMSTBBSUBS *** 4óBDOMFWIBMBSBSBTEJFMFLUSJLLBUTBZT ** :ÐLÐB[BMUMSTBEFóJõNF[ EFôFSMFSJOEFOIBOHJMFSJCVMVOBCJMJS *** -FWIBMBSBSBTQPUBOTJZFMGBSLBSUSMSTBBSUBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[** # *WF** $ *WF*** % **WF*** & * **WF*** \" :BMO[* # :BMO[** $ *WF** % *WF*** & **WF*** 3. ôFLJMEFLJTóBDOTóBT$ ZÐLÐR FOFSKJTJ&EJS 5. #JSÐSFUFDFCBóMBOBOLPOEBOTBUËSÐOTóBT$ ZÐ- C LÐR MFWIBMBSBSBTQPUBOTJZFMGBSL7EJS q q C d +– V +– 4ôBDOMFWIBMBSBSBTOEBLJV[BLMLBSUSMSTB V * $BSUBS ** q artar -FWIBMBSBSBTEV[BLMôB[BMUMSTB * $BSUBS *** &B[BMS ** RBSUBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS *** 7EFóJõNF[ \" :BMO[** # :BMO[*** $ *WF** ZBSHMBSOEBOIBOHJMFSJEPôSVEVS % *WF*** & **WF*** \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** 1. \" 2. B 3. B 75 4. \" 5. E
TEST - 6 4*ó\" 1. ,WF-LPOEBOTBUËSMFSJCJSCJSJOFTFSJCBóMPMVQ, 3. ôFLJMEFLJ, -WF.LPOEBOTBUËSMFSJË[EFõUJS, OOMFWIBMBSBSBTOBEJFMFLUSJLLBUTBZTEBIBCÐ- OO MFWIBMBS BSBTOB EJFMFLUSJL LBUTBZT EBIB LÐ- ZÐLCJSNBEEFLPOVMVZPS ¿ÐLCJSNBEEFLPOVMVZPS KL L K M +– +– V #VOBHÌSF ,WF-OJOVÀMBSBSBTOEBLJQPUBO- V TJZFMGBSL7KWF7LOBTMEFôJöJS #VOBHÌSF, -WF.OJOZÑLÑOBTMEFôJöJS RK RL RM 7K 7L \" \"[BMS \"SUBS \"[BMS # Artar Artar Artar \" \"SUBS \"[BMS $ \"[BMS %FóJõNF[ %FóJõNF[ # \"[BMS \"SUBS % %FóJõNF[ %FóJõNF[ %FóJõNF[ $ \"[BMS %FóJõNF[ & \"[BMS \"[BMS \"[BMS % \"[BMS \"[BMS & %FóJõNF[ \"[BMS 4. ±[EFõ TóB¿MBSMB LVSVMBO EFWSFEF 9: BSBTOEB- LJQPUBOTJZFMGBSL79: :;BSBTOEBLJQPUBOTJZFM GBSL7YZEJS XY Z 2. ôFLJMEFLJ LPOEBOTBUËSMFSEFO , OJO MFWIBMBS BSB- +– TOEBLJEV[BLMóBSUSMZPS V d #VOBHÌSF BOBIUBSBÀMODB79:WF7:;OBTM EFôJöJS KL M +– 79: 7:; V \" \"SUBS \"[BMS # \"[BMS \"[BMS #VOBHÌSF , - .LPOEBOTBUÌSMFSJOEFOIBO- $ \"[BMS \"SUBS HJMFSJOJOZÑLÑEFôJöNF[ % %FóJõNF[ \"[BMS & \"SUBS %FóJõNF[ \" :BMO[- # :BMO[. $ ,WF- % -WF. & , -WF. 1. B 2. B 76 3. E 4. $
4*ó\" TEST - 7 1. ôFLJMEFLJË[EFõLPOEBOTBUËSMFSJOMFWIBMBSBSBTO- 3. ôFLJMEFLJË[EFõ,WF-LPOEBOTBUËSMFSJCJSCJSJOF EB IBWB WBSES - OJO MFWIBMBS BSBTOEBLJ V[BLML QBSBMFM CBóMES ,OO MFWIBMBS BSBTOEBLJ V[BLML LпÐMUÐMÐZPS B[BMUMZPS KL d M K L +– +– V V #VOBHÌSF ,WF.LPOEBOTBUÌSMFSJOJOMFWIB- #VOBHÌSF ,WF-OJOZÑLÑJÀJOIBOHJTJEPô- MBSBSBTOEBLJFMFLUSJLBMBOMBS&KWF&MOBTM SVEVS EFôJöJS RK RL EK EM \" \"SUBS %FóJõNF[ # \"[BMS %FóJõNF[ \" \"[BMS \"SUBS $ %FóJõNF[ %FóJõNF[ # \"SUBS \"[BMS % \"SUBS \"[BMS $ \"[BMS %FóJõNF[ & \"[BMS \"SUBS % \"SUBS %FóJõNF[ & %FóJõNF[ %FóJõNF[ 2. ±[EFõ п LPOEBOTBUËS CJS ÐSFUFDF õFLJMEFLJ HJCJ 4. ôFLJM-IEF,LPOEBOTBUËSÐ7QPUBOTJZFMGBSLBM- CBóMBONõUS UOEBZÐLMFOJQ ZÐLLBZCPMNBEBOôFLJM-IIEFLJHJ- CJË[EFõ-LPOEBOTBUËSÐOFCBóMBOZPS KL K K M C C +– +– L V C V X Y #VOBHÌSFBOBIUBSBÀMEôOEB,LPOEBOTBUÌ- ôFLJMmI ôFLJMmII SÑJÀJO * :ÐLÐEFóJõNF[ #VOBHÌSF ,LPOEBOTBUÌSÑJÀJO ** -FWIBMBSBSBTOEBLJHFSJMJNEFóJõNF[ *** 4óBTEFóJõNF[ * :ÐLÐB[BMS ** 1PUBOTJZFMJB[BMS *** &OFSKJTJB[BMS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[*** $ *WF** \" :BMO[* # :BMO[*** $ *WF** % **WF*** & * **WF*** % **WF*** & * **WF*** 1. D 2. E 77 3. \" 4. E
TEST - 8 4*ó\" 1. ôFLJM-IWFôFLJM-IIEFTóBT$WF$PMBOLPO- 3. 9 : ;LPOEBOTBUËSMFSJIFSCBLNEBOË[EFõUJS EBOTBUËSMFSEFEFQPMBOBOFOFSKJMFS&1WF&2EJS XY 2C C Z +– +– V 2V +– ôFLJMmI ôFLJMmII V #VOBHÌSF E1 PSBOLBÀUS 9LPOEBOTBUÌSÑOÑOMFWIBMBSBSBTOEBLJV[BL- E2 MLBSUSMSTB * :OJOZÐLÐBSUBS \" 1 # 1 $ % & ** 9JOZÐLÐB[BMS 4 2 *** ;OJOZÐLÐEFóJõNF[ JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS \" :BMO[** # *WF** $ *WF*** % **WF*** & * **WF*** 2. ¶SFUFDF ôFLJM-I EFLJ HJCJ CBóMBOBO LPOEBOTBUËS 4. 4BCJU QPUBOTJZFM GBSL BMUOEB ZÐLMFOFO õFLJMEFLJ ZÐLMFOEJLUFOTPOSBôFLJM-IIEFLJLPOVNBZÐLLBZ- EÐ[MFNTóB¿UBEFQPMBOBOFOFSKJ&EJS C PMNBEBO HFUJSJMJZPS ôFLJM-II EF LPOEBOTBUËSÐO d MFWIBMBSBSBTOBfEJFMFLUSJLLBUTBZMNBEEFLP- OVMVZPS IBWB f ZBMULBO +– +– V +– #VOBHÌSF TôBDOMFWIBMBSBSBTOEBLJEV[BL- MôBSUUSMSLFO&FOFSKJTJOJOTBCJULBMNBTJÀJO V ôFLJMmII * -FWIBMBSOZÐ[FZBMBOBSUUSMNBM ** -FWIBMBSOZÐ[FZBMBOB[BMUMNBM ôFLJMmI *** -FWIBMBSBSBTOEBLJPSUBNOEJFMFLUSJLLBUTBZ- TBSUUSMNBM #VOBHÌSFLPOEBOTBUÌSÑO * 4óBTBSUBS JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMBCJMJS ** -FWIBMBSBSBTQPUBOTJZFMGBSLB[BMS \" :BMO[* # :BMO[** $ :BMO[*** *** -FWIBMBSEBCJSJLFOZÐLNJLUBSBSUBS JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ *WF** % *WF*** & **WF*** % *WF*** & **WF*** 1. B 2. $ 78 3. D 4. D
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF 4ôB ÷MJöLJMJ,B[BONMBS 11.2.3.7. : :ÐLMFONJõCJSTóB¿UBZÐLJMFHFSJMJNBSBTOEBLJJMJõLJZJBOBMJ[FEFS 11.2.3.8. : 4óB¿UBEFQPMBOBOFOFSKJOJOCBóMPMEVóVEFóJõLFOMFSJBOBMJ[FEFS 11.2.3.9. : 4FSJWFQBSBMFMEFWSFMFSEFFõEFóFSTóB ZÐLWFQPUBOTJZFMGBSLLBWSBNMBSJMFJMHJMJIFTBQMBNBMBSZBQBS )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. ,POEBOTBUÌSMFSJOCBôMBONBöFLJMMFSJ öLJUBOFTFSJCBóMLPOEBOTBUËSWBSTB %m/*m \"4FSJ#BôMBNB Cefl = C1.C2 C1 + C2 ++ q1 –– ++ q2 –– OUBOF$TóBMTFSJCBóMLPOEBOTBUËSWBSTB ++ –– ++ –– Cefl = C JMFCVMVOVS V1 C1 V2 C2 n +– #1BSBMFM#BôMBNB 1. 4FSJ CBóM LPOEBOTBUËSMFS TóBMBS OF PMVSTB ++ q2 –– 1. 1BSBMFMCBóMLPOEBO- PMTVOBZONJLUBSZÐLMFZÐLMFOJSMFS TBUËSMFSJOQPUBOTJZFM- ++ –– MFSJFõJUUJS 2. 4FSJCBóMBNBEBUFLCJSLPOEBOTBUËSÐOZÐLÐ BZO[BNBOEBEFWSFOJOUPQMBNZÐLÐEÐS V2 C2 71 72 7 2.1BSBMFM CBóMBNBEB q1 R2 RUPQMBN ++ q1 – 3. 4FSJ CBóM LPOEBOTBUËSMFSJO QPUBOTJZFMMFSJ EFWSFOJO UPQMBN ZÐLÐ – LPMMBSEBLJ ZÐLMFSJO UPQMBNÐSFUFDJOQPUBOTJZFMJOFFõJUUJS UPQMBNLBEBSES ++ – qUPQMBN R1 + q2 71 72 7 – 4. 4FSJ CBóMBNBEB LPOEBOTBUËSMFSJO QPUBOTJZFM V1 C1 GBSLMBSTóBMBSZMBUFSTPSBOUMES +– V q1 = V1.C14 q1 = q2 ise V1C1 = V2C2 3. 1BSBMFMCBóMLPOEBOTBUËSMFSEFWSFOJOUPQMBN q2 = V2.C2 ZÐLÐOÐTóBMBSZMBEPóSVPSBOUMQBZMBõSMBS V1 = C2 qUPQMBN R1 + q2 V2 C1 = 5. %FWSFEFLJ UÐN LPOEBOTBUËSMFSJO ZBQUó JõJ q1 = V1C14 V1 = V2 ise q1 = C1 q2 V2C2 q2 C2 UFL CBõOB ZBQBCJMFO LPOEBOTBUËSÐO TóBT- OBFõEFóFSTóB $Fõ EFOJS 4. 1BSBMFMCBóMLPOEBOTBUËSEFFõEFóFSTóB 4FSJCBóMBNBEB q1 = V1C1 _ q toplam = q1 + q2 _ q2 = V2C2 b q 1 = V1C b b 1 b b b Eflitliklerinden yararlanılarak ` Eflitliklerinden yararlanılarak ` V1 + V2 = V b q1 = q2 = qtoplambab q2 = V2C2 b V1 = V2 = V bb a V = V1 + V2 qtoplam = q1 + q2 qtoplam = q1 + q2 , q parantezine al›nd›€›nda V·Cefl = V1C1 + V2C2 , V parantezine al›n›rsa Cefl C1 C2 Cefl = C1 + C2 + . . . + Cn elde edilir. 1 = 1 + 1 + ... + 1 elde edilir. Cefl C1 C2 Cn 79
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. L ÖRNEK 49 ÖRNEK 50 4óBMBS$ $WF$PMBOLPOEBOTBUËSMFSMFLVSV- C MV,-EFWSFTJõFLJMEFLJHJCJEJS KC 4C K 2C 2C 2C C C õFLJMEFLJLPOEBOTBUÌSEFWSFTJOEF,-OPLUBMBS BSBTOEBLJFöEFôFSTôBLBÀ$EJS L %FWSFZJIBSGMFOEJSJQBÀUôN[EB #VOBHÌSF ,-OPLUBMBSBSBTOEBLJFöEFôFST- L ôBLBÀ$EJS C %FWSFZJIBSGMFOEJSJQBÀUôN[EB KK C LL 4C M M 2C C M K 2C 2C K C L LL C C L K M LL K 2C 2C 2C 4C C L C 4C KM 2C CK L 2C 2C C 4C 4C 2C K LC 2C K L=K L C C 2C 3C K L=K L C 49. 3 80 50. 2
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. ÖRNEK 51 ÖRNEK 52 4óBMBS$ $WF$PMBOLPOEBOTBUËSMFSMFLVSV- 4óBMBS $ PMBO LPOEBOTBUËSMFSMF LVSVMV EFWSFEF MBOEFWSFQBS¿BTõFLJMEFLJHJCJEJS EFWSFOJOFõEFóFSTóBT,BOBIUBSB¿LLFO$1 , BOBIUBSLBQBUMEóOEBJTF$2EJS C 2C 3C L K CC \"OBIUBS K CC #VOBHÌSF B, -OPLUBMBSBSBTOEBLJFõEFóFSTóBLB¿$EJS C\" OBIUBSB¿MODB,-OPLUBMBSBSBTFõEFóFST- +– óBLB¿$PMVS V B%FWSFZJIBSGMFOEJSJQBÀUôN[EB #VOBHÌSF C1 PSBOLBÀUS C2 C 2C 3C L \"OBIUBSBÀLLFO C LL CC 2 K C1 = C KK == C 1BSBMFMCBôM CC C 2 6C \"OBIUBSLBQBMZLFO CC 2C 2C K L=K L K = 2C 3C C\"OBIUBSBÀMODB CC = C1 = C = 1 dir. C2 C C2 = C C 2C 3C L K ,TBEFWSF .qk(7$k, ,POEBOTBUËSMFSJ¿JO 3C KL C = f A 2=$p7W = 1 C·V2 d2 $TóB 2=ZÐL 8=FOFSKJ B6 C3 81 52. 1
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. ÖRNEK 53 ÖRNEK 54 ±[EFõ, - .LPOEBOTBUËSMFSJCJSÐSFUFDFõFLJMEF- ±[EFõ LPOEBOTBUËSMFSMF LVSVMBO EFWSF õFLJMEFLJ HJ- LJHJCJCBóMBONõUS CJEJS KLM K L +– +– V V #VOBHÌSF * -FWIBMBSEBCJSJLFOZÐL ,LPOEBOTBUÌSÑOÑOZÑLÑRJTF-LPOEBOTBUÌ- ** -FWIBMBSBSBTQPUBOTJZFMGBSL SÑOÑOZÑLÑLBÀRPMVS *** ,POEBOTBUËSÐOTBIJQPMEVóVFOFSKJ ¶SFUFDJOJ¿EJSFODJËOFNTFONJZPS EFôFSMFSJOEFO IBOHJMFSJ ÑÀ LPOEBOTBUÌS JÀJOEF BZOES %FWSFTSBZMBCBTJUMFöUJSJMJSTF C CC L %FWSFIBSGMFOEJSJMJQBÀMEôOEBLPOEBOTBUÌSMFSCJSCJSJOF QBSBMFMCBôMPMVS q CK K C C L 2 3q M q L +– 2q V C ,POEBOTBUÌSMFSCJSCJSMFSJOFQBSBMFMCBôMBOEôOEBMFWIB- MBSBSBTOEBLJQPUBOTJZFMGBSLMBSFöJUPMVS 2=$p7CBôOUTOEBQBSBMFMCBôMBNBEB7TBCJUTF$TJ 2=$p7CBôOUTOEB$WF7EFôFSMFSJBZOPMEVôVJÀJO CÑZÑLPMBOLPOEBOTBUÌSÑOREFôFSJEFCÑZÑLPMVS 2 ZÑL EFôFSMFSJEFBZOPMVS W = 1 CV2 CBôOUTOBHÌSF$WF7EFôFSMFSJBZOPM- -OJOZÑLÑRPMVS 2 %m/*m EVôVJÀJOFOFSKJ 8 EFôFSMFSJEFBZOPMVS :BOU* **WF*** %Ð[MFN LPOEBOTBUËSMFS EÐõFZ PMBSBL JLJZF CËMÐOEÐóÐOEFTFSJ ZBUBZPMBSBLJLJZFCËMÐO- EÐóÐOEFQBSBMFMIBMFHFUJSJMNJõPMVS 4FSJCBóMBNB 53. * **WF*** 82 1BSBMFMCBóMBNB 54. 3
www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. ÖRNEK 55 ôJNEJCVLPOEBOTBUËSMFSJBõBóEBLJHJCJCBó- MBZBMN 4óBT$PMBOôFLJM-IEFLJLPOEBOTBUËSÐOMFWIBMBS BSBTOBEJFMFLUSJLLBUTBZTIBWBOOLJOJOJLJLBUPMBO C1, q1 ZBMULBO NBEEF LPOVMBSBL ôFLJM-II EFLJ LPOEBOTB- UËSFMEFFEJMJZPS KL dd 22 d h a W a ôFLJMmI ôFLJMmII C ,q 22 #VOB HÌSF õFLJM-II EFLJ LPOEBOTBUÌSÑO TôBT ,POEBOTBUËSMFSJO + V¿MBS,OPLUBTOB - LBÀ$EJS V¿MBS-OPLUBTOBHFMFDFLCJ¿JNEFCBóMBZB- MN#VEVSVNEBQPUBOTJZFMJ 7 ZÐLTFLPMBO õFLJM-IEFTôB C = f A EJS LPOEBOTBUËSEFOQPUBOTJZFMJEÐõÐLPMBOLPO- d EBOTBUËSF ZÐL HF¿FS ,POEBOTBUËSMFSJO TPO õFLJM-IITFSJCBôMJLJLPOEBOTBUÌSEFOPMVöVS EVSVNEBLJZÐLMFSJOJOUPQMBN a q1› + q2› k JML EVSVNEBLJ ZÐLMFSJOJO UPQMBNOB R1 + q2 dd FõJU PMBDBóOEBO WF TPO EVSVNEB QPUBOTJ- 22 C C ZFMMFSJEFFõJUPMBDBóOEBO 7,- 1 2 $1 = f A = 2 fA = 2C $2 = 2f A = 4C q1 + q2 a q1› + q2› k R $p7 d d q1 + q2 $1p7,- $2p7,- d 2 2 = 2C 4C CFö= 4C VKL = q1 + q2 PMVS 3 C1 + C2 :ÑLMÑ,POEBOTBUÌSMFSJO#BôMBONBT C1, q1 %m/*m C C KL 1 2 q1 q2 C2, q2 +– +– ,POEBOTBUËSMFSJO[ULVUVQMBS,WF-OPLUB- V1 V2 MBSOEB PMBDBL õFLJMEF CBóMBSTBL ËODF ZÐLÐ B[ PMBO LPOEBOTBUËS OËUS IBMF HFMJS ,BMBO 4óBMBS$1WF$2PMBOLPOEBOTBUËSMFSJQP- ZÐLLPOEBOTBUËSMFSJOTóBMBSPSBOOEBQBZ- UBOTJZFMMFSJ71WF72PMBOÐSFUF¿MFSFõFLJMEFLJ MBõMS HJCJCBóMBEóN[EBLPOEBOTBUËSMFSEFCJSJLFO q1 > q2 ise; ZÐLNJLUBSMBSTSBTZMBR1WFR2PMTVO,PO- EBOTBUËSMFSZÐLMFOEJLUFOTPOSBZÐLMFSJOJLBZ- q1mR2 a q › + q2› k 1 CFUNFZFDFLõFLJMEFÐSFUF¿MFSEFOTËLFMJN q1mR2 $1p7,- $2p7,- C1 C2 VKL = q1 – q2 PMVS C1 + C2 q1 q2 55. 4 83 3
11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr )(1/m6(/(5m1(<q1(/m. )(1/m6(/(5m1(<q1(/m. ÖRNEK 56 ÖRNEK 57 4óBMBS$1 =n'WF$2 = 6 n'PMBOLPOEBOTB- CK ôFLJMEFLJEFWSFEFLPO- UËSMFS QPUBOTJZFMJ71 =7PMUWF72 =7PMUPMBO EBOTBUËSMFSË[EFõ ÐSFUF¿MFSMFôFLJM-IEFLJHJCJZÐLMFOEJLUFOTPOSB $1 C 9BOBIUBSLBQBM WF$2LPOEBOTBUËSMFSJOJOZÐLMFSJLPSVOBSBL EFWSF- Y :BOBIUBSB¿LUS den TËLÐMÐQôFLJM-IIEFLJHJCJCBóMBOZPS C C1 = 4 n' C2 = 6 n' +– +– ôFLJMmI +– VX V1 = 20 V V2 = 30 V C1 #VOBHÌSFEFWSFEFÌODF9BOBIUBSBÀMQEBIB L TPOSB : BOBIUBS LBQBUMSTB ZÑL IBSFLFUJ TPO- MBOQEFOHFLPOVNVOBVMBöMEôOEB ,LPOEBO- TBUÌSÑOÑO QMBLBMBS BSBTOEBLJ QPUBOTJZFM GBSL LBÀ7PMVS K CK :BÀLLFOEFWSF öFLJMEFLJ HJCJ PMVQ EFWSFEFLJ C2 C UPQMBNZÑL +– RUPQMBN =$7+$7 ôFLJMmII V #VOB HÌSF ,- OPLUBMBS BSBTOEBLJ QPUBOTJZFM =$7EJS GBSLLBÀWPMUPMVS CK ¶SFUF¿MFSJOJ¿EJSFODJËOFNTFONJZPS 9BÀL :LBQBMZLFOEFWSF C öFLMJOEFPMVS C 7PSU = q toplam = 2CV C efl 3C õFLJM-IEF 7PSU = 2V EJS 21 =$1p71 3 = 4 n'p7 22 =$2p72 ÖRNEK 58 = 80 n$ = 6 n'p7 CVMVOVS = 180 n$ õFLJM-IIEFLPOEBOTBUÌSMFSJOBZODJOTLVUVQMBSCJSCJSJ- * coulomb joule (coulomb) 2 OFCBôMPMVQPSUBLQPUBOTJZFM volt ** *** toplam yük (volt) 2 joule VKL = eflde€er s›€a JGBEFMFSJOEFOIBOHJMFSJTôBCJSJNJPMBSBLLVMMBO- CBôOUTOEBOCVMVOVS MBCJMJS VKL = 80nC + 180nC = 26 Volt CVMVOVS *Á2=$7Á C = Q = coulomb V volt 10nF **Á W = 1 CV2 Á C = 2W = joule 2 V2 (volt) 2 ***Á W = 1 · Q2 Á C = Q2 = (coulomb) 2 2C 2W joule :BOU* **WF*** 56. 26 84 57. 2 58. * **WF*** 3
4*ó\" )EN/ISESI7ESTI 1. ,POEBOTBUÌSMFSMF LVSVMNVö öFLJMEFLJ EFWSFEF 4. ²[EFöLPOEBOTBUÌSMFSMFLVSVMNVöEFWSFEF,- FöEFôFSTôBLBÀ$EJS $BS2BJTTFF öCCE12FôPFSSBTOôLBBÀ$U1S ./BSBTFöEFôFSTôB 7C M 15C KL 3C +– V \" # $ % & N \" # 1 $ 1 % 1 & 1 2 3 4 5 2. õFLJMEFWFSJMFOLPOEBOTBUÌSMFSMFLVSVMNVöEFW- 5. õFLJMEFWFSJMFOLPOEBOTBUÌSMFSMFLVSVMBOEFWSF- SFEF,-BSBTOEBLJFöEFôFSTôBLBÀ$EJS EF,-BSBTFöEFôFSTôBLBÀ$EJS 3C 6C 4C 5C 9C 8C KL 7C 4C 3C 4C 6C 2C \" # $ % & KL \" # $ % & 6. õFLJMEFWFSJMFOLPOEBOTBUÌSMFSMFLVSVMBOEFWSF- 3. ,POEBOTBUÌSMFSMF LVSVMNVö öFLJMEFLJ EFWSFEF EF $ TôBM LPOEBOTBUÌSÑO ZÑLÑ R1 $ TôBM q1 ,-BSBTFöEFôFSTôBLBÀ$EJS LPOEBOTBUÌSÑOZÑLÑR2JTF q2 PSBOLBÀUS 6C 6C 3C 15C 12C L K 3C 4C 3C 4C \" # 6C % & \" 3 # $ 3 % 3 & 16 2 8 $ 1. $ 2. B 3. D 85 4. B 5. E 6. D
)EN/ISESI7ESTI 4*ó\" 1. ôFLJMEFWFSJMFOLPOEBOTBUËSMFSMFPMVõUVSVMNVõEFW- 4. %Ð[MFNCJSLPOEBOTBUËSÐOJMFULFOMFWIBMBSBSBTO- SFEF$TóBMLPOEBOTBUËSÐOV¿MBSBSBTOEBLJQP- EBIBWBWBSES#VLPOEBOTBUËSÐOMFWIBMBSBSBTO- UBOTJZFM GBSL 71 $ TóBM LPOEBOTBUËSÐO V¿MBS EBõFLJMEFHËSÐMEÐóÐHJCJMFWIBMBSZBSMBZBDBLõF- BSBTOEBLJQPUBOTJZFMGBSL72EJS LJMEF EJFMFLUSJL LBUTBZT IBWBOO LBU PMBO CJS 9 ZBMULBONBEEFTJLPOVMVZPS KL 4C 3C HAVA ø/2 ø/2 X–YALITKAN 2C 6C #VOBHÌSF V1 PSBOLBÀUS ,POEBOTBUÌSÑOCBöMBOHÀUBLJTôBT$JTFZFOJ V2 TôBTLBÀ$PMVS \" # 3 $ % 5 & \" # $ % & 2 2 2. ôFLJMEFWFSJMFOTFSJCBóMJLJLPOEBOTBUËSÐOFOFSKJ- MFSJ81 =+ 82 =+EÐS W1 = 3J W2 = 12J C1 C2 V1 V2 5. 4óBT $ QMBLBMBS BSBTOEBLJ QPUBOTJZFM GBSL 7 +– V PMBO CJS LPOEBOTBUËSÐO MFWIBMBSOEBO IFS CJSJOJO #V LPOEBOTBUÌSMFSJO VÀMBS BSBTOEBLJ QPUBOTJ- BMBO \" ES -FWIBMBS CBõMBOH¿UB CJSCJSJOF QBSBMFM ZFMGBSLMBSOPSBO V1 LBÀUS WF BSBMBSOEBLJ V[BLML E EJS #BõLB EFóJõJLMJL ZB- V2 QMNBEBOMFWIBMBSEBOCJSJ , LBEBSBõBóEPóSVôF- 3 \" 1 # 1 $ % & kil-IIEFLJHJCJLBZESMZPS 4 2 ++ –– ++ –– ,/3 3. ôFLJMEFLJLPOEBOTBUËSTJTUFNJOEF,BOBIUBSB¿L- , ôFLJMmII LFOTóBT$PMBOLPOEBOTBUËSEFEFQPMBOBOZÐL2 +– V EVS 4C 4C ôFLJMmI K C \"öBôEBLJMFSEFOIBOHJTJEPôSVEVS ,-FWIBMBSOCPZVEVS +– \" 4óB C PMVS # 4óB 2 CPMVS 2 3 Üreteç $ 4óB C PMVS % 4óB 3 CPMVS #VOBHÌSF ,BOBIUBSLBQBUMSTBTJTUFNJOUPQ- 3 2 MBNZÑLÑLBÀ2PMVS \" # $ % & & 4óB$PMVS 1. B 2. \" 3. $ 86 4. $ 5. B
%·;(·/&-&,53÷,\"-\"/7&4*ó\" KARMA TEST - 1 1. 4ôBÀMBSMBJMHJMJ 6. ,POEBOTBUÌSMFSMF JMHJMJ WFSJMFO CJMHJMFSEFO IBO- * öLJ BEFU ZBMULBO QMBLBOO BSBTOEB JMFULFO CJS HJTJZBOMöUS NBEEFWBSES \" ,VUVQTV[LPOEBOTBUËSMFS%$WFZB\"$EFWSFMF- ** &MFLUSJL FOFSKJTJOJ FMFLUSJL BMBO PMBSBL EFQPMB- SJOEFLVMMBOMBCJMJS ZBOEFWSFFMFNBOES # &MFLUSPMJUJL WF UBOUBM LPOEBOTBUËSMFS LVUVQMVEVS *** #JSJNJ'BSBEES WF%$JMF¿BMõS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS $ ,POEBOTBUËSMFSLTBTÐSFMJóJOFZÐLEFQPFEFS \" :BMO[* # :BMO[*** $ *WF** % öLJ MFWIBEB FõJU NJLUBSEB FMFLUSPOB TBIJQ JLFO % **WF*** & * **WF*** LPOEBOTBUËSEPMVEVS 2. 'PUPôSBG NBLJOBMBSOO GMBöOEB LVMMBOMBO ö- & -FWIBMBSBSBTHFSJMJN QJMHFSJMJNJOFFõJUPMEVóV BOEBHF¿FOBLNTGSES ôOCJSBOEBQBSMBNBTOTBôMBZBOEFWSFFMFNB- OBöBôEBLJMFSEFOIBOHJTJEJS \" %JSFO¿ # ¶SFUF¿ $ 4óB¿ 7. )BWBPSUBNOEBCVMVOBOCJSLPOEBOTBUÌSÑOT- % 3FPTUB & 5SBOTGPSNBUËS ôBTOBSUUSNBLJÀJO * -FWIBMBSBVZHVMBOBOQPUBOTJZFMGBSLBSUUSNBL 3. 5FNFMPMBSBLLPOEBOTBUËSFMFLUSJLZÐLMFSJOJLTBTÐ- ** -FWIBMBSOZÐ[FZBMBOOBSUUSNBL *** -FWIBMBSBSBTOBZBMULBOCJSNBEEFZFSMFõUJSNFL SFMJóJOFEFQPFEFCJMFOFMFLUSPOJLEFWSFFMFNBOES JöMFNMFSJOEFOIBOHJMFSJUFLCBöOBZBQMBCJMJS #VOBHÌSFLPOEBOTBUÌS * 'PUPóSBGNBLJOFTJGMBõõóOOZBONBT \" :BMO[*** # *WF*** $ *WF** ** )PQBSMËSEFCBTWFUJ[TFTMFSJOFMEFFEJMNFTJ % **WF*** & * **WF*** *** 3BEZPMBSEBQBSB[JUFOHFMMFNF JöMFNMFSJOEFOIBOHJMFSJOEFLVMMBOMS \" :BMO[* # :BMO[** $ *WF** % **WF*** & * **WF*** 8. ôFLJM-IEFLJTóBT$1PMBOLPOEBOTBUËSÐOMFWIB- 4. * &OFSKJEFQPMBNB MBS BSBTOEB IBWB CPõMVóV WBSES -FWIBMBSO BSB- TôFLJM-IIEFLJHJCJDBNMFWIBJMFEPMEVSVMEVóVOEB ** ,PNQBO[BTZPO LPOEBOTBUËSÐOTóBT$2PMVZPS *** %PóSVMUNB JöMFNMFSJOEFOIBOHJMFSJOEFLPOEBOTBUÌSMFSLVM- C1 C2 MBOMS A AA A \" :BMO[* # *WF** $ *WF*** d1 = d d2 = d % **WF*** & * **WF*** ôFLJMmI ôFLJMmII 5. ,FOEJTJOJ CFTMFZFO LBZOBL UÑLFOEJôJ [BNBO #VOBHÌSF C2 PSBOBöBôEBLJMFSEFOIBOHJTJOJ C1 IBG[BTOEBLJCJMHJZJLBZCFEFOBMFUMFS DFQUFMF- WFSJS GPOV EJKJUBMLPMTBBUJWC JÀJOHFÀJDJEFPMTBÀÌ- [ÑN PMVöUVSBO CB[ WFSJMFSJO LBZCPMNBTO FO- \" $BNMFWIBOOBMBOO HFMMFZFOFMFLUSPOJLEFWSFFMFNBOBöBôEBLJMFS- # $BNONPMFLÐMLÐUMFTJOJ EFOIBOHJTJEJS $ $BNOIBWBZBHËSFEJFMFLUSJLLBUTBZTO % $BNMFWIBOOLBMOMóO \" 1JM # ,POEBOTBUËS & $BNOTBóMBNMLEFSFDFTJOJ $ %JSFO¿ % %JZPU & 5SBOTGPSNBUËS 1. D 2. $ 3. E 4. E 5. B 87 6. D 7. D 8. $
KARMA TEST - 2 %·;(·/&-&,53÷,\"-\"/7&4*ó\" 1. ôFLJMEFLJÐSFUFDFCBóM 4. \"öBôEBLJMFSEFOIBOHJTJTôBCJSJNJEFôJMEJS EÐ[MFNLPOEBOTBUËSÐO d * joule ** c joule 2 MFWIBMBSBSBTOEBLJ coulomb volt V[BLMLEEJS +– m V E BSUSMEôOEB BöB- *** joule *7 coulomb ôEBLJ OJDFMJLMFSEFO ^volth2 volt IBOHJTJEFôJöNF[ \" :BMO[* # :BMO[** $ *WF** \" ,POEBOTBUËSÐOTóBT % ***WF*7 & * ***WF*7 # ,POEBOTBUËSEFEFQPMBOBOFOFSKJ $ ,POEBOTBUËSÐOFMFLUSJLZÐLÐ % -FWIBMBSBSBTOEBLJFMFLUSJLBMBOOCÐZÐLMÐóÐ & -FWIBMBSBSBTOEBLJQPUBOTJZFMGBSL 2. 7HFSJMJNJOEFEPMEVSVMBO +– 5. 4óBT$PMBOIBWBMLPOEBOTBUËSCJSLBZOBLZBS- V LPOEBOTBUËS ÐSFUF¿UFO ENZMB7QPUBOTJZFMJBMUOEBZÐLMFOJZPS,POEBO- BZSMBSBL MFWIBMBSOO TBUËSLBZOBLUBOBZSMNBEBOLPOEBOTBUËSMFWIBMBS BSBTOB EJFMFLUSJL LBUTB- BSBTOBEJFMFLUSJLLBUTBZTIBWBOOLJOJOLBUPMBO ZTEBIBCÐZÐLCJSNBE- ZBMULBOCJSNBEEFLPOVMVZPS EFLPOVMVZPS #VOBHÌSF #VOBHÌSF * ,POEBOTBUËSÐOMFWIBMBSBSBTOEBLJQPUBOTJZFM * 4óB GBSLEFóJõNFNJõUJS ** (FSJMJN ** ,POEBOTBUËSÐOTóBTLBUOB¿LNõUS *** -FWIBMBSBSBTOEBLJFMFLUSJLBMBO *** ,POEBOTBUËSÐOEFQPMBZBDBóZÐLLBUOB¿L- NõUS *7 &OFSKJ OJDFMJLMFSJOEFOIBOHJMFSJB[BMS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # *WF** $ ** ***WF*7 % **WF*** & * **WF*** % * **WF*7 & * ***WF*7 3. f 4óBT $ PMBO LPOEBO- 6. õFLJMEFLJ LPOEBOTBUÌSÑO BLÑ JMF + – TBUËS TBCJU 7 HFSJMJNJ BM- – A UOEBZÐLMFOJZPS CBôMBOUT LFTJMEJLUFO TPOSB MFW- + – d -FWIBMBSBSBTV[BLMô + – ZBSZBEÑöÑSEÑôÑNÑ[- +– EFBöBôEBLJMFSEFO IBMBS CJSCJSJOF ZBLMBöUSMSTB BöB- + V IBOHJTJHFSÀFLMFöJS ôEBLJ OJDFMJLMFSEFO IBOHJTJ EFôJ- $ 4óB \" Artar öJS + – # Artar $ Artar * Elektrik alan AKÜ 12V % \"[BMS & \"[BMS 2 :ÐL & &MFLUSJL\"MBO ** 4óB \"[BMS Artar Artar Artar *** 1PUBOTJZFMGBSL %FóJõNF[ \"[BMS \"[BMS %FóJõNF[ *7 :ÐLNJLUBS \"[BMS \"[BMS \" *WF** # **WF*** $ *WF*** % * **WF*7 & ** ***WF*7 1. E 2. $ 3. B 88 4. $ 5. E 6. B
%·;(·/&-&,53÷,\"-\"/7&4*ó\" KARMA TEST - 3 1. ôFLJMEFLJ TóB¿ MFW- 4. ôFLJMEFLJ TóBDO TóBT $ f IBMBS BSBTOEB EJF- ZÐLÐR QPUBOTJZFMGBSL7EJS +– MFLUSJL LBUTBZT f V +– #VOBHÌSF MFWIBMBSBSBTO- PMBO NBEEF WBSLFO EBLJ ZBMULBO PSUBNO EJF- ZÐLMFOJZPS¶SFUF¿UFO V MFLUSJLLBUTBZTBSUUSMSTB BZSMNBEBO EJFMFLUSJL NBEEFBMOZPS * $BSUBS #VOBHÌSF TôBDOTôBT ZÑLÑWFEFQPFEJMFO ** RBSUBS QPUBOTJZFMFOFSKJOBTMEFôJöJS *** 7EFóJõNF[ 4óB Yük &OFSKJ ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" \"[BMS Artar %FóJõNF[ # Artar \"[BMS \" :BMO[* # :BMO[** $ :BMO[*** $ \"[BMS \"[BMS \"[BMS % \"[BMS \"[BMS %FóJõNF[ % *WF** & * **WF*** & Artar Artar \"[BMS 5. x Artar A ôFLJMEFLJ QBSBMFM QMBLBM CJS TóBDO QMBLBMBSOO 2. + – ôFLJMEFLJTóB¿7HF- BMBO \" BSBMBSOEBLJ SJMJNJ BMUOEB ZÐLMFO- +– NJõUJS V[BLMLYPMVQCVQMBLBMBS +– (FSJMJNB[BMUMEôO- + – QPUBOTJZFMGBSL7PMBOCJS V EB V QJMFõFLJMEFLJHJCJCBóMBO- NõUS1JMFCBóMJLFOBSBMBSOEBLJV[BLMLYPMVO- DBZBLBEBSQMBLBMBSCJSCJSMFSJOEFOV[BLMBõUSMZPS * 4óBDOZÐLÐ #VOBHÌSF ** 4óBDOTóBT *** 4óB¿UBEFQPFEJMFOFOFSKJ * 4óBDOTóBT OJDFMJLMFSJOEFOIBOHJMFSJB[BMS ** -FWIBMBSBSBTOEBLJFMFLUSJLBMBO *** 4óBDOZÐLÐ \" :BMO[** # *WF** $ *WF*** OJDFMJLMFSJOEFOIBOHJMFSJB[BMS % **WF*** & * **WF*** \" :BMO[ZÐL # :BMO[FMFLUSJLBMBO $ :BMO[TóB % 4óBWFZÐL 3. :ÐL #JSLPOEBOTBUËSFBJU & 4óB ZÐLWFFMFLUSJLBMBO yük -QPUBOTJZFMGBSL b HSBGJóJ õFLJMEFLJ HJ- CJEJS a 1PUBOTJZFM (SBGJLUFBWFCEF- 6. #JS TôBDO TBCJU QPUBOTJZFM GBSL BMUOEB EBIB GBSL ôFSMFSJ CJMJOEJôJOF HÌSF GB[MBZÑLEFQPMBZBCJMNFTJJÀJO * -FWIBMBSBSBTOBEJFMFLUSJLLBUTBZTEBIBLÐ- * ,POEBOTBUËSCLBEBSZÐLMÐJLFOFOFSKJTJ ¿ÐLCJSPSUBNLPZNBL ** ,POEBOTBUËSÐOTóBT ** -FWIBMBSCJSCJSJOFZBLMBõUSNBL *** -FWIBMBSOZÐ[FZBMBOMBSOLпÐMUNFL *** ,POEBOTBUËSÐOMFWIBMBSBSBTV[BLML JöMFNMFSJOEFOIBOHJMFSJZBQMNBMES OJDFMJLMFSJOEFOIBOHJMFSJCVMVOBCJMJS \" :BMO[* # :BMO[** $ *WF** \" :BMO[* # :BMO[** $ :BMO[*** % **WF*** & * **WF*** % *WF** & **WF*** 1. D 2. $ 3. $ 89 4. E 5. E 6. B
)EN/ISESI.ARMA7ESTI %·;(·/&-&,53÷,\"-\"/7&4*ó\" 1. NLÐUMFMJ ZÐLMÐDJTJNZBMULBOCJS a 4. 5.10-5$MVLZÑLMÑQBSÀBDô X 8 cm Y 3 cm q B JQMF CBóMBOBSBL EÐ[HÐO FMFLUSJL QBSBMFM MFWIBMBS BSBTOEB BMBOJ¿FSJTJOFTBSLUMEóOEBõF- m \"EBO #ZF HÌUÑSNFL JÀJO A 4 cm LJMEFLJHJCJEFOHFEFLBMZPS FMFLUSJL LVWWFUMFSJOF LBSö –+ N H aBÀTWFRCJMJOFOMFSJZMF ZBQMBOJöLBÀKPVMFPMVS BöBôEBLJMFSEFOIBOHJTJCVMV- V = 8000V OBCJMJS \" # $ * &MFLUSJLTFMLVWWFU % & ** &MFLUSJLBMBO 5. + + + + + + + + + *** $JTNJOZÐLÐOÐODJOTJ \" :BMO[* # :BMO[** $ *WF*** E\" m q d –+ % **WF*** & * **WF*** V ––––––––– 2. :Ð[FZBMBOMBS\" LBm +– A õFLJMEF EÑöFZ EÑ[MFNEF QBSBMFM EVSBO MFWIBMBS d BSBTOEBEFOHFEFLBMBCJMFONLÑUMFMJ(BôSMLMWF MOMLMBS Y BSBMBSO- RZÑLMÑQBSÀBDLJÀJO EBLJ V[BLML E PMBO A x * ' ( V ** R& NH QBSBMFMMFWIBMBS7QP- UBOTJZFM GBSLOB CBó- *** RZÐLÐOÐOJõBSFUJ ES MBOBSBLZÐLMFONJõUJS *7 q = mgd &MFLUSJLBMBOöJEEFUJBöBôEBLJMFSEFOIBOHJTJOF V CBôMEFôJMEJS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS * 7QPUBOTJZFMGBSLOB '=FMFLUSJLTFMLVWWFU H=ZFS¿FLJNJWNFTJ ** EV[BLMóOB \" *WF** # * **WF*7 $ ** ***WF*7 *** \"ZÐ[FZBMBOOB *7 YLBMOMóOB % * **WF*** & * ***WF*7 \" :BMO[* # *WF** $ * **WF*** % ***WF*7 & ** ***WF*7 6. %ÐõFZ EÐ[MFNEF CVMVOBO QBSBMFM mq –+ V 3. :BOEBLJ öFLMF HÌSF , m L K L M \" E1 MFWIBMBSBSBTOEBLJ E RZÐLÐEFOHFEFEJS QBSBMFM MFWIBMBS BSBTO- -FWIBMBSBSBTOEB- LJ FMFLUSJL QPUBOTJZFMJ 7 JTF FMFLUSJL BMBO &\" ZJ EBLJ FMFLUSJL BMBO öJEEFUJ 2 cm 3 cm CVMNBLJÀJO E1 = 105 /$ - m . MFW- E2 IBMBS BSBTOEBLJ FMFLU- * R QBS¿BDóOZÐLÐ –+ SJLBMBOöJEEFUJE2 = 3.105 V2 ** H ZFS¿FLJNJWNFTJ /$ JTF ÑSFUFÀMFSJO QP- *** '\" FMFLUSJLTFMLVWWFU UBOTJZFM GBSLMBS PSBO V1 +– *7 N QBS¿BDóOLÐUMFTJ LBÀUS V2 V1 OJDFMJLMFSJOEFOIBOHJMFSJOJOCJMJONFTJHFSFLMJWF A 1 # 2 $ 2 % 3 & 9 ZFUFSMJEJS 3 9 3 24 \" :BMO[* # :BMO[*** $ *WF*** % **WF*7 & * ***WF*7 1. E 2. D 3. B 90 4. \" 5. B 6. $
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)EN/ISESI.ARMA7ESTI %·;(·/&-&,53÷,\"-\"/7&4*ó\" 1. 4óBMBS $ PMBO JLJ LPOEBO- K C 4. C2 = C C TBUËSQPUBOTJZFMGBSL7PMBO C1 = 4C LBZOBL ZBSENZMB ZÐLMFO- NJõLFO TJTUFNJO EFQPMBEó FOFSKJ8EJS ,BOBIUBSBÀMSTBTJTUFN- +– C3 = 3C EFEFQPMBOBOFOFSKJLBÀ8 V +– PMVS 8V $ 1 % 1 & 1 õFLJMEFLJEFWSFEF$1LPOEBOTBUÌSÑOEFEFQPMB- 2 48 \" # OBOFOFSKJ81 $3LPOEBOTBUÌSÑOEFEFQPMBOBO FOFSKJW2JTF W1 PSBOLBÀUS W2 \" # 2 $ 3 D 3 & 4 3 2 43 2. ôFLJMEFLJHJCJTFSJCBóMJLJLPOEBOTBUËSÐOFOFSKJMFSJ 5. 6C 3C TSBTZMB81 =-2+ 82 =-2+EÐS 4C W = 2·10–2 J W = 5·10–2 J 10C C1 C2 +– V +– V õFLJMEFTôBT$PMBOLPOEBOTBUÌSÑOMFWIBMBS BSBTOEBLJQPUBOTJZFMGBSL7PMEVôVOBHÌSF C ÑSFUFDJOQPUBOTJZFMGBSL 7 LBÀWPMUUVS #VLPOEBOTBUÌSMFSJOTôBMBSOOPSBO 1 LBÀUS \" # $ % & C 2 \" # $ % & 6. ¶¿EÐ[MFNLPOEBOTBUËSMFLVSVMBOõFLJMEFLJFMFLUSJL EFWSFTJOEF$1 $2 $3TóBMLPOEBOTBUËSMFSJOZÐL- leri TSBTZMB21 22 23 QPUBOTJZFMGBSLMBS71 72 73UÐS C1= 3C C2= 6C 3. ôFLJMEFHËSÐMFOQBSBMFMCBóMLPOEBOTBUËSMFSJOZÐL- V1 V2 C3= 2C leri q1 = 2n$ R2 =n$EVS q1 C1 q2 C2 V3 + – +– V V #VOBHÌSF C #VLPOEBOTBUÌSMFSJOTôBMBSOOPSBO 1 LBÀUS * 21 22 23 ** 71 72 73 C *** 21 22 23 FöJUMJLMFSJOEFOIBOHJMFSJZBOMöUS 2 \" # $ % & 1 \" :BMO[* # :BMO[** $ :BMO[*** 4 % *WF** & **WF*** 1. $ 2. $ 3. E 92 4. E 5. E 6. $
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