سلسلة تمارين في الفيزياء حول دراسة الظواهر الكهربائية من اعداد الاستاذ فرقاني ف

12 : 2011/2010 : - (03) – -I0 = E → E = RI0 : ‫ا‬- R :‫ﻡ ا ن‬ :‫و‬E = 50 . 0.2 = 10Vτ = 5 . 10-3 sτ = RC → C = τ : ‫ا ا وﻡ‬ ‫ ﺕ غ ا‬-‫ أ‬-2 RC = 5 .10-3 = 10-4 F = 100 µF 50 : uC ‫ﺏ‬ ‫ ا د ا‬-‫ب‬ : ‫ﻥ ن ﺝ ا ﺕ ات‬uAB = uAM + uMB . ‫و ه ﻡ د ﺕ ﻡ ا رﺝ ا و‬0=Ri+u dqR dt + u = 0 d(C u)R +u=0 dt duRC + u = 0 dt : ‫دا‬ ‫ ه‬u = Ee-t/τ ‫ ا ﻡ‬-‫ﺝـ‬u = Ee-t/τdu = - E e-t/τ = - E e‫ـ‬t / τdt τ RC : ‫ا دا‬ ‫ﺏ‬- E e-t/τ + 1 Ee-t/τ = 0 →0=0 RC RC . ‫دا‬ ‫إذن ا ا ه‬ : E ، τ' ، t ‫ و‬lnu ‫ ا رة ا ﺏ‬-‫ أ‬-3 :u = Ee-t/τ' . ،، :– –lnu = ln(Ee-t/τ')lnu = lnE + lne-t/τ' :

13 : 2011/2010 : - (03) – - t : τ -‫د‬lnu = lnE - τ' :‫ﻡ ا ن‬ ‫ﺏ ﺏ ﻡا ا‬ tlnu = - τ + lnE : C’lnE = at + b : ‫اﺏﻥ‬ 1 → τ' = - 1- τ' = a a 0 - 2.3 → τ' = - 1 = 10-3 sa = 2.3.10-3 - 0 = -1000 - 1000τ' = R’C → C = τ' R'C = 10‫ـ‬3 = 2 .10-5 F = 20 µF 50 ** ‫ ﻥ رس‬: ‫** ا ذ‬ ‫ﻥ ﺝ إﺏ‬ ‫ﻥ ﻡد ﻥ ﺏ‬ - ‫ا وب‬ [email protected] Tel : 0771998109 . ‫ا ا وﻥ ﺏ ي ﺥ ا روس أو ا ر و‬ ‫وﺵ ا ﻡ‬ : ‫ أدﺥ ﻡ ا ذ‬. ‫ﻥ ﻡ ه ا ا ع و‬ sites.google.com/site/faresfergani : . ،، :– –

‫اا‬ ‫را ا ا‬ ‫ا‬ ‫ﻥ ﻡد‬‫– ا وب‬ ‫ﻥﺏ‬ ‫وزارة ا ﺏ ا‬‫ا ذ ‪ :‬ﻥ رس‬ ‫دة ا م ا‬ ‫إن‬ ‫ا‬ ‫‪:‬ا ما وا‬ ‫ا‬ ‫ا ة‪ 3:‬ت‬ ‫م‪3:‬عت‪،‬ر‪،‬تر‬‫‪Sujet : 3AS 03 - 04‬‬ ‫‪ :‬درا اه آ ‪.‬‬ ‫ا يا‬‫ا ا را ‪2011/2010 :‬‬ ‫‪2011/03/10 :‬‬ ‫ر‬‫رة ) ‪، q(t) = 10-3 ( 1 – e-50 t‬‬ ‫א ن א ول ‪ ) :‬اﻡ ن ا ا ‪(**) ( 2009/2008 -‬‬ ‫)‪ (C‬و ﻥ أوﻡ ﻡ وﻡ ‪R‬‬ ‫ﻥ ا ارة ا ﺝ ﻥ ﺏ ل ﻡ‬ ‫و ﻡ ﺕ ا آ ا ﺏ ‪ E‬آ ا ﺏ ﺵ ا اﻥ‬ ‫ﻡ ا ‪.t=0‬‬ ‫ا ‪،‬ﻡ‬ ‫ﺏ ‪ uC‬ا ﺕ ﺏ‬ ‫‪ -1‬أ‪ -‬أوﺝ ا د ا‬ ‫ﺡ دون أي ﺏ ه ن ‪.‬‬ ‫ا ﺏ ‪ q‬ا ﻥ أﺡ‬ ‫ب‪ -‬أآ ا رة ا‬ ‫ا ﺏ ﺏ ﺏ ا ﻡ ‪ τ‬و ‪ Q0‬ﺵ ا ا ا ﺕ‬ ‫ﻥا ‪.‬‬ ‫ا ‪t‬ﺕ ﺏ‬ ‫‪ -2‬إن ا ا ﺏ ا ﻥ أﺡ ا‬ ‫ا ﻡذ ‪:‬‬ ‫ا‪.‬‬ ‫أ‪ -‬ا ا ‪Q0‬‬ ‫ب‪ -‬ﺏ ا ﻡ ‪.‬‬ ‫ب‪ -‬ا ‪ t1‬ا ا ﺕ ن ا ﻡ ﻥ ﺏ ﺵ ا ‪.‬‬ ‫ه ‪ C = 100 µF‬أوﺝ ‪:‬‬ ‫‪ -3‬أن ا ا‬ ‫أ‪ -‬ﻡ ار ا ة ا آ ا ﺏ ‪. E‬‬ ‫ب‪ -‬ﻡ وﻡ ا ا وﻡ ‪. R‬‬ ‫ﻥا ‪.‬‬ ‫ﺝـ‪ -‬ا ا ﺏ ا ﻥ ا‬ ‫‪ ) :‬اﻡ ن ا ا – ‪(**) ( 2009/2008‬‬ ‫א نא‬ ‫ا ا ‪ ،‬ﺡ ‪. r = 10 Ω ، L = 1 H :‬‬ ‫ﻥ اآ ا‬ ‫‪YA L , r‬‬ ‫‪E‬‬ ‫‪R‬‬ ‫‪YB‬‬‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪2:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (04‬‬ ‫‪–-‬‬‫ا ‪t=0‬‬ ‫ا )‪.(1‬‬ ‫ا ﺥ ‪ YA‬ا ن ا‬ ‫‪ -1‬ا ‪ t = 0‬ﻥ ا ‪k‬‬ ‫أ‪ -‬أآ رة ا ﺕ ا ﺏ ﺏ‬ ‫ا ﺵ ﺏ ا ﻡ ‪.E،r،R،t‬‬ ‫ﺏ ‪.E‬‬ ‫‪0.2‬‬ ‫‪1.66‬‬ ‫ا ﺥ ‪ . YA‬أوﺝ ﻡ ﺥ ‪:‬‬ ‫ب‪ -‬ﻡ ذا ا ن ا ي‬ ‫‪ -‬ا ﺕ ا ﺏ ‪.E‬‬ ‫‪ -‬ﺵ ة ا ر ا ر ا ارة ا م ا ا ‪.‬‬ ‫‪ -2‬ﻥ ا و ﻥ ﻡ ﺕ ر ا ا ﺏ ا ﻥ ا ﺵ ﺏ ا ﻡ )ا ‪.(2‬‬‫ه ‪. i(t) = I0 e-t/τ :‬‬ ‫ﺏ ‪ i‬و ‪ ، di/dt‬أ أﻥ ﺡ‬ ‫ام ﻥ ن ا ﺕ ات أآ ا د ا‬ ‫أ‪ -‬ﺏ‬ ‫‪.‬‬ ‫ا )‪ E(L‬ا ﻥ ا ﺵ‬ ‫‪t‬ﺏ ‪.E،r،R،L،t‬‬ ‫ﺝـ‪-‬‬ ‫ا ﻡ ‪،τ‬وﺵةا ر ا‬ ‫دا ا )‪ (2‬أوﺝ ‪ :‬آ ﻡ ﺏ‬ ‫د‪ -‬إ‬ ‫هـ‪ -‬أوﺝ ا وﻡ ‪ R‬ا وﻡ ‪.‬‬ ‫א ن א ‪ ) :‬اﻡ ن ا ا ﻥ – ‪(**) ( 2010/2009‬‬‫‪ C‬و ﻥ أوﻡ‬ ‫ﻥ ﻡ ﻡ ﺕ ﺏ ‪ E=6V‬و ﻡ‬ ‫ا )‪ (1‬و ا‬ ‫ا ارة ا ﺏ ا‬ ‫‪.‬‬ ‫ارة ﺏ )‪ q(t‬ﺥ ل ﺵ ا‬ ‫ﻡ وﻡ ‪.R‬‬ ‫ﻥ ن ا ﺕ ات‪ ،‬ﺝ ا د ا‬ ‫‪ -1‬ﺏ‬ ‫‪ -2‬ﺏ أن ﺡ ه )‪.q(t)=Q0(1- e-t/τ‬‬ ‫‪ -3‬ا )‪ (2‬ﺕ ر ﺵ ا ‪:‬‬‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪3:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (04‬‬ ‫–‬ ‫‪-‬‬ ‫‪+‬‬ ‫ﺏ اﻡ‪.‬‬ ‫أ‪ -‬أوﺝ‬‫‪EG‬‬ ‫ا ‪ 99%‬ﻡ ا ا ؟ ﺏ ر إﺝ ﺏ ‪.‬‬ ‫ب‪ -‬ه ا ﻡ ‪ 0,05s‬آ‬ ‫‪-‬‬ ‫‪ ،‬ﻡ وﻡ ا ا وﻡ ‪ ،‬ﺵ ة ا ر ا م ا ا ‪.‬‬ ‫آ ﻡ‪ :‬ا‬ ‫‪-4‬‬ ‫ا ﻥ ا‪.‬‬ ‫ا اﻥ‬ ‫‪-5‬‬ ‫א ن א א ‪ ) :‬ض ا ا ﻥ – ‪(**) ( 2009/2008‬‬ ‫‪:‬‬ ‫ا ا ﺝ ةا‬ ‫ا ‪ 1-‬دارة آ ﺏ ﺕ‬ ‫اآ ا‬ ‫‪k‬‬ ‫‪ -‬وﺵ ) ‪ ( B‬اﺏ ) ‪. ( L , r‬‬ ‫••‬ ‫‪ -‬ﻥ أوﻡ ﻡ وﻡ ‪B R = 40 Ω :‬‬ ‫‪R‬‬ ‫ﺕ ا آ ا ﺏ ‪E = 12 v‬‬ ‫‪ -‬ﻡ ) ‪ ( G‬ذو ﺕ ﺕ ﻡ‬ ‫‪k-‬‬ ‫ا ‪ ، t = 0 :‬و ﻥ ﺏ ﺕ رات ﺵ ة ا ر ا رة‬ ‫ﻥا‬ ‫ا ن ا ) ا ‪( 2-‬‬ ‫ﺏ ارة‬ ‫)‪i( mA‬‬ ‫‪50‬‬ ‫)‪t(ms‬‬ ‫‪5‬‬ ‫ا ‪2-‬‬ ‫‪3-‬‬ ‫)‪L(H‬‬ ‫ة ا ر ا رة ا ارة‬ ‫‪ – 1‬أوﺝ ا رة ا‬ ‫)‪τ(ms‬‬‫‪146x10-3‬‬ ‫ﺏ ‪ E،L،r،R،t‬ا ما ﻥ ‪.‬‬ ‫‪5‬‬ ‫ة ا ر ا رة‬ ‫‪ – 2‬أ ‪ -‬أآ ا رة ا‬ ‫ا ارة ا م ا ا و أﺡ ا د‬ ‫ب– ا ‪r‬‬ ‫‪ – 3‬أ– أوﺝ ﺏ ل ا ن ﺏ ا ﻡ ‪ τ‬ا‬ ‫ب– ا ‪L‬‬‫‪50x10-3‬‬ ‫‪–4‬ﻥ و تﻡ ﻡ ر ا ن‪L=f(τ):‬‬ ‫) اﻥ ا ‪( 3-‬‬ ‫‪3‬‬ ‫ﺏ أن ه ا ﺏ ﺕ ﻥ ا ‪ r‬ا ﺏ‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪4:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (04‬‬ ‫–‬ ‫‪-‬‬ ‫א ن א س‪(**) :‬‬ ‫ﻡ ﺕﺕﻡ ﻡ ﺕ‬ ‫ا‬ ‫دارة آ ﺏ ﺕ‬ ‫ا آ ا ﺏ ‪ . E‬ﻥ أوﻡ ﻡ وﻡ ‪ ، R‬وﺵ‬ ‫)‪. (L , r = 10Ω‬‬ ‫ا ‪ t = 0‬و ﻥ ﺏ ﺕ ات ا ﺕ ‪ uMa‬ﺏ‬ ‫ﻥا‬ ‫ا ﺵ ﺏ ا را اه از‬ ‫ا وﻡ ‪ uBM‬ﺏ‬ ‫ﺵﺵ ا ﻥ ا ‪.‬‬ ‫وا ي‬ ‫‪ -1‬أﺡ ‪. E‬‬ ‫‪ -2‬أﺡ ‪. L ، R‬‬ ‫ا ‪. t = 3 ms‬‬ ‫‪ i‬ﺏ ) ‪ ( r , E , L , R‬و اﺡ‬ ‫‪-3‬‬ ‫ا ﺏ‪.‬‬ ‫‪ -4‬أﺡ ا ا ﻥ ا ﺵ ﻥ ا‬ ‫‪ -5‬ﺏ ا ﻡ ارة ‪.‬‬ ‫** ا ذ ‪ :‬ﻥ رس **‬ ‫ﻥ ﻡد ﻥ ﺏ‬ ‫ا وب ‪-‬‬ ‫‪[email protected]‬‬ ‫‪Tel : 0771998109‬‬ ‫ا روس أو ا ر و ﺡ ‪.‬‬ ‫ا ا وﻥ ﺏ ي ﺥ‬ ‫ﻥ ﺝ إﺏ‬ ‫وﺵ ا ﻡ‬ ‫ﻥ ﻡ ه ا ا ع و ‪ .‬أدﺥ ﻡ ا ذ ‪:‬‬ ‫‪sites.google.com/site/faresfergani‬‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

5: 2011/2010 : - (04) – - ‫أﺝ ﺏ‬Sujet : 3AS 03 - 04 . ‫ درا اه آ‬: ‫ا يا‬uE = uR + uC (**) ( 2009/2008 - ‫ ) اﻡ ن ا ا‬: ‫א ن א ول‬E=Ri+u : uC ‫ إ د ا د ﺏ‬-‫ أ‬-1 dqR +u=E : ‫و ه ﻡ د ﺕ ﻡ ا رﺝ ا و ﺕ ا ا‬ dt d(C u)R +u=E dtdu 1 E + u=dt RC RC - 1 t uC = E (1- e τ ) : q ‫ ا رة ا ﻡ ـ‬-‫ب‬q = C uC - 1 tq = C E ( 1 - e τ ) - 1 tq = Q0 (1- e τ ) - . ‫ ه ﺵ ا ا‬Q0 = CE : ‫ﺡ‬ : τ ‫ و‬Q0 -‫ أ‬-2q = 10-3 ( 1 - e-50t ) : : ‫ﺏ ﺏ ﻡا ا ا ﺏ‬▪ Q0 = 10-3 C▪ 1 = 50 → τ = 1 = 0.02 s τ 50 : ‫ ا ﺕ ن ا ﻡ ﻥ ﺏ ﺵ ا‬t1 ‫ا‬t = t1 → q= Q0 2 : ‫ ا ﺏ‬q ‫رة‬ ‫ﺏ‬ : . ،، :– –

6: 2011/2010 : - (04) – -Q0 - 1 t1 2 = Q0 ( 1 - e τ ) - 1 t1 11 - e τ = 2 - 1 t1 1 1e τ =1- = 22 11- τ t1 = ln 2 1 = - ln2 → t1 = τ ln2- τ t1t1 = 0.02 ln2 = 1.39 .10-2 sQ0 = CE → E = Q0 : E ‫ ﻡ ار‬-3 C : ‫( ن‬q ‫ﻡ ) رة‬ 10-3 : ‫ ﻡ وﻡ ا ا وﻡ‬-‫ب‬E = 10-4 = 10 V : ‫ ا ا ﺏ ا ﻥ ﻥ ا‬-‫ﺝـ‬τ = RC → R = τ : ‫ وﻡ‬uC = E : ‫ﻥ ا‬ CR = 0.02 = 200 Ω 10‫ـ‬4E(C) = 1 C u 2 2 CE(C) = 1 C E2 2E(C) = 1 .10-4 (10)2 = 5 .10-3 J 2 (**) ( 2009/2008 – ‫ ) اﻡ ن ا ا‬: ‫א نא‬ :E،L،r،R،t ‫ا ﺵ ﺏ‬ ‫ رة ا ﺕ ﺏ‬-1 : diuL = L dt + r i : . ،، :– –

7: 2011/2010 : - (04) – -i = I0 ( 1 - e-t/τ ) : ‫ﺡ ﻥ ن ﺝ ا ﺕ ات‬E = uL + uRuL = E - uR ( 1 – e-t/τ)uL = E – RI0uL = E - RE (1- e-t/τ ) R+ruL = E - RE - RE e-t/τ R+r R+ruL = ER + Er - RE - RE e-t/τ R+r R+ruL = Er - ER e-t/τ R+r R+r : t = 0 uL ‫ رة‬-t=0 → E r E R E(R + r) =E uL = R +r - R +r = R +r .. ‫ا ﺵ‬ ‫ ا ﺕ ﺏ‬yA ‫ا ﺥ‬ ‫ ا ن ا ي‬-‫ب‬t = 0 → u = uL = 6 V :E -t = 0 → uL = E : (1) ‫ﻡ ا‬ :‫و ﺏ‬ . E = 6V : ‫إذن‬ : ‫ﺵةا ر ا ما ا‬- di : (2) ‫ا م ا ا و ﻡ ا‬uL = L dt + r iuL(∞) = 0.2 V : ‫آﺏ‬ ‫ ا ﺏ‬uL ‫رة‬ ‫دا‬ ‫وا‬ ‫ وﻡ‬di = 0 ، i = I0 ‫ن‬ (t = ∞) ‫ا م ا ا‬ dtuL(∞) = r I0 → I0 = u L(∞ ) r 0.2 : ‫ ا د ا‬-‫ أ‬-2I0 = 10 = 0.02 A : ‫ﺡ ﻥ ن ﺝ ا ﺕ ات‬0 = uL + uR : . ،، :– –

8: 2011/2010 : - (04) – - di . ‫و ه ﻡ د ﺕ ﻡ ا رﺝ ا ﻥ‬L + r i + Ri = 0 : ‫ ه ﺡ د ا‬i = I0e-t/τ ‫ إ ت أن‬- dt diL + (R + r) i = 0 dtdi (R + r) + i=0dt Li = I0e-t/τ = E r e-t/τ R+di = - I0 e-t/τ =- E R+r e-t/τ = - E e-t/τdt τ R+r L L : ‫ا دا‬ ‫ﺏ‬- E e-t/τ + R + r . E e-t/τ = 0 . ‫إذن ا ا ه ﺡ د ا‬ L L R+r- E e-t/τ + E e-t/τ = 0 → 0 = 0 LL : ‫ رة ا ا ﻥ‬-‫ب‬E(L) = 1 L i2 2E(L) = 1 L (I0e-t/τ )2 2E(L) = 1 L I02 e-2t/τ 2 :‫ﺏ اﻡ‬ : (2) ‫ﻡ ا‬τ = 1.66 .10-3 s → τ = 2 .1.66 .10-3 = 2.32 .10-3 s :‫ا‬ ‫ﺵةا ر‬-2 : E(L) ‫رة‬ t=0 ‫ﺏ‬E(L)(0) = 1 L I02 → I0 = 2 E(L)(0) 2 Lt = 0 → E(L) = E(L)(0) = 2 . 10-4 J : (2) ‫ﻡ ا‬ : ‫وﻡ‬ : . ،، :– –

9: 2011/2010 : - (04) – - 2 . 2 .10-4I0 = = 0.02 A 1 : ‫ ﻡ وﻡ ا ا وﻡ‬- E → E → EI0 = R + r R +r = R= -r I0 I0R = 2 6 - 10 = 290 Ω .10-2 (**) ( 2010/2009 – ‫ ) اﻡ ن ا ا ﻥ‬: ‫א ن א‬ : ‫ ا د ا‬-1 : ‫ﺡ ﻥ ن ﺝ ا ﺕ ات‬uE = uL + uR q dqE= +R C dtdq 1 E . ‫و ه ﻡ د ﺕ ﻡ ا رﺝ ا و‬dt + RC q = R : ‫ إ ت ﺡ ا د‬-2q = Q0 (1 - e-t/τ ) = EC (1 - e-t/τ )dq = EC e-t/τ = EC e-t/τ = E e-t/τdt τ RC R : ‫ا دا ﻥ‬ ‫ﺏ‬E e-t/τ + 1 EC (1 - e-t/τ ) = ER RC RE e-t/τ + E (1- e-t/τ ) = ERR RE e-t/τ + E - E e-t/τ = E → EE =R RR R RR . ‫إذن ا ا ه ﺡ د ا‬ : ‫ ﻡ ا ا و ﻥ‬99% : ‫ ﺏ ا ﻡ‬-‫ أ‬-3 . τ = 0.01 s : ‫ ن‬q = f(t) ‫ﻡ ﺥ ل ا ن‬ ‫ ﺕ ا‬t = 0.05 s ‫ ﻡ ا ن أن ا‬-‫ب‬ 0.05 -t = 0.05 → q = Q0 (1 - e 0.01 ) = 0.99 Q0 .‫ا‬ ‫ ﻡ ا‬99% ‫ا‬ ‫ آ ف‬0.05 s ‫أن ا ﻡ‬ : . ،، :– –

‫‪10 :‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (04‬‬ ‫–‬ ‫‪-‬‬‫‪Q0 = EC‬‬ ‫→‬ ‫‪C = Q0‬‬ ‫‪ -4‬ا ‪:‬‬ ‫‪E‬‬ ‫ﻡ ا ن ‪ Q0 = 6 . 10-7 C :‬وﻡ ‪:‬‬‫‪C = 6 .10-7 = 10-7 F‬‬ ‫‪ -‬ﻡ وﻡ ا ا وﻡ ‪:‬‬ ‫‪6‬‬‫‪τ = RC → R = τ‬‬ ‫‪C‬‬‫‪R‬‬ ‫=‬ ‫‪0.01‬‬ ‫‪= 105‬‬ ‫‪Ω‬‬ ‫‪7‬ـ‪10‬‬ ‫‪ -‬ﺵ ة ا ر ا ﺏ ا م ا ا ﺕ ن ﻡ وﻡ ن ا ر ا ﺏ دارة ا اﻥ ء‬ ‫ا‪.‬‬ ‫‪ -5‬ا ا ﻥ ا ‪:‬‬‫)‪E(C‬‬ ‫=‬ ‫‪1‬‬ ‫‪C‬‬ ‫‪u‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪C‬‬ ‫ن ‪ uC = E :‬وﻡ ‪:‬‬ ‫ﻥا‬‫)‪E(L‬‬ ‫=‬ ‫‪1‬‬ ‫‪E2‬‬ ‫‪2C‬‬‫‪E(L) = 0.5 .10-6 . (6)2 = 1.8 .10-6 J‬‬ ‫א ن א א ‪ ) :‬ض ا ا ﻥ – ‪(**) ( 2009/2008‬‬ ‫ة ا ر ا ر ا ارة ﺏ ‪ E ، L ، r ، R ، t‬ا م ا ﻥ ‪:‬‬ ‫‪-1‬أ‪ -‬ا رة ا‬ ‫=‪i‬‬ ‫‪E‬‬ ‫‪R+r‬‬ ‫‪-t‬‬ ‫‪R+r‬‬ ‫‪eL‬‬ ‫ب‪: r -‬‬ ‫ﻡ ا رة ا ﺏ ‪:‬‬ ‫‪E‬‬ ‫ب‪: r -‬‬‫‪t = ∞ → i = I0 = R + r‬‬ ‫‪ -3‬أ‪ -‬ﺏ ا ﻡ ‪: τ‬‬‫‪I0‬‬ ‫=‬ ‫‪E‬‬ ‫→‬ ‫=‪R+r‬‬ ‫‪E‬‬ ‫‪→ r= E -R‬‬ ‫ﻡ ا ن‪:‬‬ ‫‪R+r‬‬ ‫‪I0‬‬ ‫‪I0‬‬‫‪r = 12 - 40 = 8 Ω‬‬ ‫‪0.25‬‬‫‪τ = 2 . 10-3 = 10-2 s‬‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

11 : 2011/2010 : - (04) – -τ = L → L = τ (R + r) : L -‫ب‬ R+rL = 10-2 (40 + 8) = 0.48 HL=aτ : ‫ إ ت أن ا ﺏ ﺕ ﻥ ا‬-‫ب‬ : ‫ﺏﻥ‬L = (R + r) τ :‫ﻥ‬R+r=a → r=a–R :‫ﺏ ﺏ‬ 144 - 0 → r = 48 – 40 = 8 Ω . ‫وه ﻥ ا ا ﺏ‬a = 3.10-3 - 0 = 48uBA = uBM + uMA (**) ( 158/02 – 01 ‫ ع ف‬3 ) :‫א ن א س‬E = uBM + uMA : E ‫ ﺡ ب‬-1E = uBM0 + uMA0 : ‫ﺡ ﻥ ن ﺝ ا ﺕ ات‬uMA0 = 7 V :‫و ا ما ا ن‬uBM0 = 2V → E = 2 + 7 = 9 V :‫ﻡ ا ﻥ وه ا ما ا ن‬ di : L ، R ‫ ﺡ ب‬-2uBM = L dt + ri :uMA = R i :‫و ا ما ا ن‬uBM0 = r I0uMA0 = R I0uBM0 = r → R = r uMA0uMA0 R u BM0R = 10 . 7 = 35 Ω 2 : . ،، :– –

12 : 2011/2010 : - (04) – - :L : di :‫ ن‬t=0 ‫ا‬uBM = L dt + r i di : ‫ ن‬uMA(t) ‫ﻡ ا ن‬(uBM )t=0 = L(dt )t=0 + r i(t=0) : ‫ ن‬uMA = Ri : ‫و ﺡ أن‬t = 0 → uMA = 0 : ‫وﻡ‬i(t = 0) = (uMA )t=0 = 0 = 0 R 35(u BM = di → (u BM )t=0 )t=0 L( )t L = di ..................... (1) dt =0 (dt )t=0 . di ، (uBM)t=0 : ‫ﻥ‬ (dt )t=0 : (uBM)t=0 ▪ . (uBM)t=0 = 9V : ‫ ن‬uBM = f(t) ‫ﻡ ا ن‬ : di ▪ (dt )t=0( du MA )t =0 = tanα = 7-0 = 3500 : ‫ ه‬uMA = f(t) ‫ﻡ ا ن‬ dt 2 .10-3 - 0 :‫وﻥ‬uMA = R i→ du MA di dt =R :‫ ن‬t=0 ‫و ا‬ dt( du MA )t=0 = di → di = 1 ( du MA )t=0 dt R(dt )t=0 (dt )t=0 R dt di 1 : (1) L ‫رة‬ ‫ﺏ‬(dt )t=0 = 35 . 3500 = 100 9L = = 0.09 H 100 : . ،، :– –

13 : 2011/2010 : - (04) –- : ( r ، E ، L ، R) ‫ ﺏ‬i ‫ رة‬-3 i(t) = E R+r -t R+r (1-e L ) : t = 3 . 10-3 s ‫ ا‬i - : ‫ا رة ا ﺏ‬ ‫ﺏ‬ 9 - 35+10 ‫ـ‬ 3 .3.10i(t) = ( 1 - e 0.09 ) = 0.155 A 35 +10 : t = 3 . 10-3 s ‫ ا ا ﻥ ا ﺵ ا‬-4 : ‫ ﺏ ا ﻡ‬-5E(L) = 1 (0.155)2 = 1.1.10-3 J . 0.09 2τ = L r R+τ = 0.09 = 2 .10-3 s 35 +10 ** ‫ ﻥ رس‬: ‫** ا ذ‬ ‫ﻥ ﻡد ﻥ ﺏ‬ - ‫ا وب‬ [email protected] Tel : 0771998109 . ‫ا روس أو ا ر و ﺡ‬ ‫ا ا وﻥ ﺏ ي ﺥ‬ ‫ﻥ ﺝ إﺏ‬ ‫وﺵ ا ﻡ‬ : ‫ أدﺥ ﻡ ا ذ‬. ‫ﻥ ﻡ ه ا ا ع و‬ sites.google.com/site/faresfergani : . ،، :– –

‫اا‬ ‫را ا ا‬ ‫ا‬ ‫ﻥ ﻡد‬‫– ا وب‬ ‫ﻥﺏ‬ ‫وزارة ا ﺏ ا‬‫ا ذ ‪ :‬ﻥ رس‬ ‫دة ا م ا‬ ‫إن‬ ‫ا‬ ‫‪:‬ا ما وا‬ ‫ا‬ ‫ا ة‪ 3:‬ت‬ ‫م‪3:‬عت‪،‬ر‪،‬تر‬‫‪Sujet : 3AS 03 - 05‬‬ ‫‪ :‬درا اه آ ‪.‬‬ ‫ا يا‬‫ا ا را ‪2011/2010 :‬‬ ‫‪2011/03/10 :‬‬ ‫ر‬ ‫א ن א ول ‪:‬‬ ‫‪12‬‬ ‫اﺏ‬ ‫)ا ‪ (1-‬ﻡ ا‬ ‫ﺕ ن ا ارة ا ﺏ ا‬ ‫‪D 1-‬‬ ‫ا‬ ‫ا‪:‬‬ ‫اﻡ‬ ‫‪+‬‬ ‫‪R‬‬ ‫▪ ﻡ ﺕ ا آ ا ﺏ ‪E = 12 V‬‬‫‪E‬‬ ‫‪A‬‬ ‫▪ﻡ ‪.C‬‬ ‫ـ‬ ‫‪C‬‬ ‫▪ ﻥ أوﻡ ﻡ وﻡ ‪. R = 200 Ω‬‬ ‫‪B‬‬ ‫▪ﻡ ‪.K‬‬ ‫‪ K‬ا )‪ (1‬ﺏ ﻥ دارة‬ ‫ا ‪ ، t = 0s‬ﻥ ا‬ ‫ﺏ ا ا ه از ا ‪ ،‬ﻡ‬‫ﺕ را ﺕ ا ﺏ ﺏ‬ ‫ا‬ ‫ﺏ أن ﻥ ﺏ‬ ‫ا‬ ‫)ا ‪. (2-‬‬ ‫)‪ uc =f(t‬وا‬ ‫ا‬ ‫ا ‪02‬‬ ‫‪:‬‬ ‫ا ﺕ ﺏ ﺏ ‪ uC‬و ‪ t‬ﺕ ﺏ‬ ‫ﻥ ن ﺝ ا ﺕ ات ‪ ،‬أ أن ا د ا‬ ‫‪ -1‬ﺏ‬‫‪. t =0‬‬ ‫) ‪du C (t‬‬ ‫‪+‬‬ ‫‪1‬‬ ‫=‬ ‫‪E‬‬ ‫‪:‬‬ ‫‪dt‬‬ ‫)‪R.C .uC (t‬‬ ‫‪R.C‬‬ ‫‪ -2‬أ ﺏ ا ي أن ا ﺏ ‪ τ‬ر ﺏ ﻥ ا ا و ﺡ ات ‪.‬‬ ‫ا ﺏ ه ‪ ، uC (t) =E(1-e-t/τ) :‬ﺏّ أن ‪ uC = 0 :‬ا‬ ‫‪ -3‬ﺕ أن ﺡ ا د ا‬ ‫‪ -4‬ﻡ ه ﺵ ة ا ر ا ﺏ ا ر ا ارة ﺏ ‪ ∆t = 60 ms‬ﻡ ؟ ‪.‬‬ ‫‪t =5 τ ، t = τ :‬‬ ‫ا ﺕ ‪ uc‬ا‬ ‫‪ -5‬أﺡ‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪2:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (06‬‬ ‫–‬ ‫‪-‬‬ ‫‪ ّ -6‬ﻡ ا ن ا ﺏ ‪. τ‬‬ ‫ا ‪.C‬‬ ‫‪ -7‬أوﺝ‬ ‫‪ ) :‬ﺏ ر ‪ – 2010‬م ﺕ ( )**(‬ ‫א نא‬ ‫دارة آ ﺏ‬ ‫ﻥ ﺕ )‪ (L,r‬ﻡ ﺕ وﺵ ﻥ ﺏ‬ ‫ا ﻡ‪:‬‬ ‫‪ -‬ﻡ آ ﺏ ذي ﺕ ﺕ ﺏ ‪. E = 6V‬‬ ‫‪ -‬ﻥ أوﻡ ﻡ وﻡ ‪. R = 10 Ω‬‬ ‫‪) k -‬ا ‪. (1-‬‬ ‫‪ -1‬ﻥ ا ‪ ، k‬اآ رة آ ﻡ ‪:‬‬ ‫ا ا وﻡ ‪. R‬‬ ‫‪ : uR‬ا ﺕ ا ﺏ ﺏ‬ ‫اﺵ ‪.‬‬ ‫‪ : ub‬ا ﺕ ﺏ‬ ‫ر ا ﺏ )‪ i(t‬ا ر ا ارة ‪.‬‬ ‫ﻥ ن ﺝ ا ﺕ ات ‪ ،‬أوﺝ ا د ا‬ ‫‪ -2‬ﺏ‬ ‫‪E‬‬ ‫‪-‬‬ ‫)‪(R +r‬‬ ‫‪t‬‬ ‫‪.‬‬ ‫= )‪i(t‬‬ ‫‪(1- e‬‬ ‫‪L‬‬ ‫)‬ ‫‪:‬‬ ‫ا ﺏ ﺕ ﺡﻡا‬ ‫‪ -3‬ﺏ أن ا د ا‬ ‫‪R+r‬‬ ‫‪ -4‬ﻡ ا را ا‬ ‫ﺏ ﺏ ﺕ ر ﺵ ة ا ر ا ﺏ ا ر ا ارة و ر ا ن ا‬ ‫)ا ‪. (2-‬‬ ‫ﺏ ﻥ ﺏ ن أﺡ ‪:‬‬ ‫أ‪ -‬ا وﻡ ‪ r‬ﺵ ‪.‬‬ ‫‪ L‬ذاﺕ ا ﺵ ‪.‬‬ ‫ب‪ τ -‬ﺏ ا ﻡ ‪ ،‬ا‬ ‫ﻥ ا ﺵ ﺡ ا ما ا ‪.‬‬ ‫ا ا ﺏا‬ ‫‪ -5‬أﺡ‬ ‫( )**(‬ ‫א ن א ‪ ) :‬ﺏ ر ‪ – 2010‬م ﺕ‬ ‫دارة آ ﺏ ﺕ ن ﻡ ‪:‬‬ ‫ﻥ‬ ‫ذو ﺕ ﺕ آ ﺏ ﺏ ‪. E = 5V‬‬ ‫•ﻡ‬ ‫•ﻥ‬ ‫أوﻡ ﻡ وﻡ ‪. R = 100 Ω‬‬ ‫•ﻡ‬ ‫‪.C‬‬ ‫‪.k‬‬ ‫•‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪3:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (06‬‬ ‫–‬ ‫‪-‬‬ ‫ا ‪ B ، A‬إ واﺝ دﺥ ل ز إ م‬ ‫ﻥ‬ ‫ا ت ﺏ ﻡ \"‪\"MicrosfteExcel‬‬ ‫و‬ ‫ا ﻥ )‪) uC = uAB = f(t‬ا ‪. (2-‬‬ ‫ا‬ ‫وﺕ‬ ‫ارة ﻡ اﺕ ا ر ﻡ ﺏ آ ﻡ‬ ‫‪ /1‬ا ح ﻡ‬ ‫ا ﺕ ‪ uR‬و ‪. uC‬‬ ‫ﺏ ا ﻡ ‪τ‬وﻡ ﻡ ا ؟ا‬ ‫‪/2‬‬ ‫ا ‪.C‬‬ ‫ﺏ غ ا ارة م ا ا ‪.‬‬ ‫‪ /3‬أﺡ ﺵ ا‬ ‫‪ ، C' = 2C‬أر‬ ‫‪ /4‬ا ا ا ﺏ ﺏ‬ ‫ا ﺏﺵ ا‬ ‫آ‪ ،‬ﻥا‬ ‫)‪ uC' = g(t‬ا ي ﻡ ه ﺕ ﺵ ﺵ ا ز ‪ .‬ﻡ ا ‪.‬‬ ‫א ن א א ‪ ) :‬ﺏ ر ‪ – 2010‬ر ت ( )**(‬ ‫اﻡ‬ ‫ﺏ ضﺵ ﻡ ر ‪،C ،‬ﻥ‬ ‫ا ﺏا ‪:‬‬ ‫ا‬ ‫‪ -‬ﻡ ذو ﺕ ﺕ آ ﺏ ﺏ ‪ E = 5V‬و ﻡ وﻡ ا اﺥ ﻡ ‪.‬‬ ‫‪ -‬ﻥ أوﻡ ﻡ وﻡ ‪. R = 120 Ω‬‬ ‫‪ -‬ﺏ د ‪) k‬ا ‪. (2-‬‬ ‫اﺏ‬ ‫‪ -1‬ﺏ ﺕ ر ا ﺕ ا ﺏ ‪ uC‬ﺏ‬ ‫او‬ ‫رﺏ‬ ‫ا ﻡ ‪،‬ﻥ ﻡ س‬ ‫ا ‪ ، t = 0‬ﻥ ا د ا )‪. (1‬‬ ‫ةﻡ وﺏ هةﺵ ا ﺏ ء‬ ‫ﺕ ﺕ ﺵﺵ ﺝ زا ﻡ ا‬ ‫ا‬ ‫وﺏ‬ ‫ا ا‪:‬‬ ‫)‪t (ms‬‬ ‫‪0 4 8 16 20 24 32 40 48 60 68 80‬‬ ‫)‪uC (V‬‬ ‫‪0 1.0 2.0 3.3 3.8 4.1 4.5 4.8 4.9 5.0 5.0 5.0‬‬ ‫‪.‬‬ ‫ا‪. C‬‬ ‫أ‪ /‬أر ا ن )‪. uC = f(t‬‬‫‪ ،‬أﻥ‬ ‫ا ‪ RC‬و ا‬ ‫ﺏ اﻡ‪τ‬‬ ‫ب‪ /‬ﺏ ﻥ‬ ‫‪:‬‬ ‫ﺏ اﻡ ‪ τ‬ا ؟‬ ‫‪ -2‬آ ﺕ‬ ‫'‪ C‬ﺡ ‪ C' > C‬و ‪. R = 120 Ω‬‬ ‫‪ -‬ا )أ(‪ :‬ﻡ أﺝ ﻡ‬ ‫''‪ C‬ﺡ ‪ C'' = C‬و ‪. R' < 120 Ω‬‬ ‫‪ -‬ا )ب(‪ :‬ﻡ أﺝ ﻡ‬ ‫)أ( و )ب( ا ﺏ‬ ‫‪ uC‬ا‬ ‫)‪ (2) ، (1‬ا‬ ‫أر آ ‪ ،‬ﻥ ا ا‬ ‫‪. dq(t) +‬‬ ‫‪1‬‬ ‫‪E‬‬ ‫رة ‪:‬‬ ‫ﺏ‬ ‫ة )‪ q(t‬ﺕ‬ ‫ا‬ ‫‪-3‬أ‪ /‬ﺏ أن ا د ا‬ ‫= )‪q(t‬‬ ‫ب‪ /‬ﺡ ا د ا‬ ‫‪dt RC‬‬ ‫‪R‬‬ ‫ﺏ رة ‪ q(t) = Aeαt + β‬ﺡ ‪ A‬و ‪ α‬و ‪ β‬اﺏ ﺕ‬ ‫ا ‪ t = 0‬ﺕ ن ‪. q(t) = 0‬‬ ‫ﻥ ه آ إ زﻡ ‪.‬‬ ‫‪ -4‬ا ﻡ ﻥ ﻥ ا د ا )‪(2‬‬ ‫ا ‪ t = 0‬ا ا ﺏ ا ﻥ ‪ E0‬ا ‪.‬‬ ‫أ‪ /‬أﺡ‬ ‫‪ E = E0‬؟‬ ‫ب‪ /‬ﻡ ه ا ﻡ ا ي ﻡ أﺝ ﺕ ا ا ﻥ ا‬ ‫‪2‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

‫‪4:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (06‬‬ ‫–‬ ‫‪-‬‬ ‫א ن א س ‪ ) :‬ﺏ ر ‪ – 2010‬ر ت ( )**(‬ ‫ا ﺏا ‪:‬‬ ‫ﻥﺏ ا ا‬ ‫• ﻥ أوﻡ ﻡ وﻡ ‪. R = 500 Ω‬‬ ‫‪ C‬ﻡ ﻥ‪.‬‬ ‫•ﻡ‬ ‫• ﻡ ذي ﺕ ﺕ آ ﺏ ﺏ ‪. E‬‬ ‫• ‪) k‬ا ‪. (2-‬‬ ‫ﻡ ﻡ ﺏ ﺕ ر ا ﺕ ا ﺏ )‪ uC(t‬ﺏ ا‬ ‫ﺏ ا ن )ا ‪. (3-‬‬ ‫ﻡ ا ﺕﺏ‬ ‫ﺵا‬ ‫‪-1‬‬ ‫‪ 99%‬ﻡ ا ﺕ ا ﺏ ﺏ‬ ‫ا‪.‬‬ ‫ا دا ا ن ‪:‬‬ ‫ﺏ ا ﻡ ‪τ‬و ا ﺕ ا ﺏ‬ ‫أ‪/‬‬ ‫ا ‪.C‬‬ ‫ا أﺡ‬ ‫ﺏ‬ ‫ب‪ /‬ﺡ د ا ة ا ﻡ '‪ t‬آ ل ﺵ ا‬ ‫‪.‬‬ ‫ﺝـ‪ /‬ﻡ ه ا ﺏ '‪ t‬و ‪ τ‬؟‬ ‫ﻥ ن ﺝ ا ﺕ ات أوﺝ ا د‬ ‫‪ /2‬ﺏ‬ ‫ا‪:‬‬ ‫ﺏ ا ﺕا ﺏ ﺏ‬ ‫ا‬ ‫‪ ، uAB = uC‬ﺏ أﻥ ﺕ ﺡ ﻡ ا ‪:‬‬ ‫) ‪. uC = E(1- e-t/τ‬‬ ‫ا ا ﺏ ا ﻥ ‪EC‬‬ ‫‪ /3‬أوﺝ‬ ‫ا ت ‪. t2 = 5τ ، t1 = τ ، t0 = 0 :‬‬ ‫ا‬ ‫)‪. EC = f(t‬‬ ‫‪ /4‬ﺕ )ر آ ( ﺵ ا‬ ‫** ا ذ ‪ :‬ﻥ رس **‬ ‫ﻥ ﻡد ﻥ ﺏ‬ ‫ا وب ‪-‬‬ ‫‪[email protected]‬‬ ‫‪Tel : 0771998109‬‬ ‫ا روس أو ا ر و ﺡ ‪.‬‬ ‫ا ا وﻥ ﺏ ي ﺥ‬ ‫ﻥ ﺝ إﺏ‬ ‫وﺵ ا ﻡ‬ ‫ﻥ ﻡ ه ا ا ع و ‪ .‬أدﺥ ﻡ ا ذ ‪:‬‬ ‫‪sites.google.com/site/faresfergani‬‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬

5: 2011/2010 : - (06) – - ‫أﺝ ﺏ‬Sujet : 3AS 03 - 06 . ‫ درا اه آ‬: ‫ا يا‬ : ‫א ن א ول‬ : ‫ ا د ا‬-1 : ‫ﻥ ن ا ﺕ ات‬ ‫ﺏ‬UDB = UDA + UABE = R.i + UC (t) : ‫ ن‬i = dq = C. duC : ‫و ﺡ‬ dt dtE = RC du C + uC dt E = du C + 1R.C dt R.C .uCdu C + 1 = E dt R.C .u C R .C : ‫ ر ﺏ ﻥ‬τ ‫ إ ت أن‬-2[τ] = [R][C] [Q] [U] [Q] ‫ ر ﺏ ﻥ‬τ ‫وﻡ‬[τ] = [I] = [I][∆t] → [τ] = [∆t] : ‫ ا ﻡ ﺡ ا د‬-3 [I] [U] = [I]uC = E(1 - e-t/τ )duC = E e-t/τ dt τ : ‫ا دا ﻥ‬ ‫ﺏ‬E e-t/τ + 1 E (1- e-t/τ ) = Eτ RC RCE e-t/τ E - E e-t/τ E → EEτ + RC RC = RC RC = RC . ‫إذن ا ا ه ﺡ د ا‬ :‫ه ا ن‬ : 60ms ‫ ﺵ ة ا ر ﺏ‬-4 ‫ ﺕ ن ا ارة ﺡ ا م ا ا و‬60 ms ‫ﺏ‬ : . ،، :– –

6: 2011/2010 : - (06) – -i = dq = C duC = 0 . ‫ ﺏ ا م ا ا‬uC ‫ن ا ﺕ‬ dt dt :t=5τ،t=τ ‫ ا‬uC ‫ ا ﺕ‬-5t = τ → u = 12(1‫ ـ‬e‫ـ‬1) = 7.6Vt = 5τ → u = 12(1‫ ـ‬e‫ـ‬5) = 11.9V : ‫ ﺏ ا ﻡ‬-6 . τ = 9 . 10-3 s = 9 ms : ‫ ﻥ‬uc = f(t) ‫ا ن‬ uC = 7.6 V ‫ﺏ ط ا‬ : C ‫ ا‬-7τ = RC → C = τ Rc = 9×10‫ـ‬3 = 45×10‫ـ‬6 F = 45µF 200 : ‫א نא‬ : ub ، uR ‫رة‬ -1 uR = Ri ‫ ا‬-2 di ‫ﺡ‬ ub = L dt + r i : ‫دا‬ : ‫ﻥ ن ﺝ ا ﺕ ات‬ di uE = ub + uRE = L dt + r i + R i . ‫و ه ﻡ د ﺕ ﻡ ا رﺝ ا و‬ diL + (R + r)i = E dtdi (R + r) E + i=dt L L : i(t) = E (R +r) ‫ﺕا‬ ‫ إ ت ان ا د ا‬-3 -t R+r (1-e L )i(t) = E (R +r) -t R+r (1-e L )di(t) E R + r - (R + r) t E ‫ـ‬ (R + r ) t = L L . e = edt R + r L L : . ،، :– –

7 : 2011/2010 : - (06) – - : ‫ا دا‬ ‫ﺏ‬E (R +r) + R +r E (R +r) = E -t -t L eL (1-e L )L L R+rE - (R +r) t + E (1- (R +r) t ) = E L - eLL eL LE (R +r) + E - E (R +r) E → EE -t -t = = eL eLL LL L LL . ‫إذن ا ا ه ﺡ د ا‬imax = I0 = 0.5A : ‫ ﺵ‬r ‫ ا وﻡ‬-4 :‫ﻡ ا ن‬ E → E → r= E -R :‫و‬I0 = R + r R+r= I0 I0 : L ‫ و‬τ -‫ب‬ ‫و ا‬t=0 ‫▪ا لﻡ ا س ا‬r = 6 -10 = 2 Ω 0.5 :▪ . τ ≈ 10 ms : ‫ ﻥ‬I0 ‫( ﻡ‬63%) ‫ا‬ : ‫ ا ا ﻥ ا ﺵ ا م ا ا‬-5τ = L → L = τ (R + r) :‫و ا ما ا ن‬ R+r : ‫א نא‬L = 10 .10-3(10 + 2) = 0.12 H : ‫ ﻡ ا ارة‬-1E(L) = 1 L i2 2E(L) = 1 L I02 2E(L) = 1 . 0.12 (0.5)2 = 1.5 .10-2 J 2 : . ،، :– –

‫‪8:‬‬ ‫‪2011/2010 :‬‬ ‫)‪- (06‬‬ ‫–‬ ‫‪-‬‬ ‫‪ -2‬ﺕ ‪: τ‬‬‫‪t = τ → uC = 0.63 . uC0 = 0.63 E = 0.63 . 5 = 3.15 V‬‬ ‫ط‬ ‫ﺏ‬ ‫ا ن ﻥ ‪. τ = 10-3 s = 1 ms :‬‬ ‫ا‬ ‫ا‬ ‫ل ﻥ ا ﺏ س ا ن )‪ uC = f(t‬ا ‪. t = 0‬‬ ‫لا‬ ‫‪:‬‬ ‫ه ا ﻡ ا زم ا ﺏ ‪ 63%‬ﻡ ﺵ ا ‪.‬‬ ‫ا‪:‬‬‫‪τ = RC → C = τ = 10-3 = 10-5 F = 10 µF‬‬ ‫ﺏ غا ما ا ‪:‬‬ ‫‪ -3‬ﺵ ا‬ ‫‪R 100‬‬ ‫ا ‪ Q0‬ﺡ ن ‪:‬‬ ‫ﺏ غ ا م ا ا أي ﻥ ا ﺕ ﺵ ا‬‫‪Q0 = EC‬‬‫‪Q0 = 5 . 10-5 = 5 . 10-5 C‬‬ ‫‪: C' = 2C‬‬ ‫‪ -4‬ا ن )‪ u'C = f(t‬ا ال ا ا ﺏ ﺏ‬ ‫د ﻡ ا أي ‪ τ = a C‬و ‪:‬‬ ‫ﺏ اﻡ‬‫‪C' = 2C → τ' = 2τ‬‬‫إﺕ م ا ( ا ن ا ن ا ا‬ ‫داد زﻡ إﺕ م ا )أو ﺕ ﺥ‬ ‫ه ا أن ‪ τ‬ﺕ داد و ﺏ‬ ‫ـ '‪ τ‬آ ‪:‬‬‫‪t = τ → uC 0.63 uC0 = 0.63 . 5 = 3.15 V‬‬ ‫א نא א ‪:‬‬ ‫س ا ‪) t = 0‬ا ( ‪.‬‬ ‫‪ -1‬أ‪ /‬ا ن )‪: uC = f(t‬‬ ‫ب‪: C ، τ -‬‬ ‫ﺏ ط ا ن ﻥ ‪. τ ≈ 15.6 ms :‬‬ ‫ا ل ﻥ ا ﺏ لا‬‫‪τ = RC‬‬ ‫→‬ ‫=‪C‬‬ ‫‪τ‬‬ ‫‪15.6‬‬ ‫‪. 10-3‬‬ ‫‪= 15.6 .10-5‬‬ ‫‪F = 156 µF‬‬ ‫=‬ ‫‪R 100‬‬ ‫‪:‬‬ ‫‪. ،،‬‬ ‫–‪:‬‬ ‫–‬