MARINE ELECTRO-TECHNIQUE 1

Chapter 2 • For single-voltage-source dc circuits, conventional current flow always passes from a low potential to a high potential when passing through a voltage source Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 • Conventional current flow always passes from a high to a low potential when passing through a resistor for any number of voltage source in the same circuit. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 SERIES RESISTOR The total resistance of resistors in series is the sum of the individual resistors. RT = R1 + R2 + R3 + R4 + ... + RN For example, the resistors in a series circuit are 680 , 1.5 k, and 2.2 k. What is the total resistance? R1 VS 680 4.38 k 12V R2 1.5k Principles of Electric Circuits - Floyd R3 © Copyright 2006 Prentice-Hall

Chapter 2 Example Determine the total resistance of the series connection in Figure 1. Figure 1 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 SERIES RESISTOR Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter S2 ERIES CIRCUITS Series circuit rule for current: Because there is only one path, the current everywhere is the same. For example, the reading on the first ammeter is 2.0 mA, What do the other meters read? 2.0+mA _2.0 mRA1 + VS 2.0 mA 2.0 mA + _© Copyright 2006 Prentice-Hall _Principles of Electric Circuits - Floyd

Chapter 2 Measuring the current throughout the series circuit Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 SERIES CIRCUITS  Total resistance (RT) is all the source ‡sees.·  Once RT is known, the current drawn from the source can be determined using Ohm¶s law: Is = Vs RT  Since Vs is fixed, the magnitude of the source current will be totally dependent on the magnitude of RT . Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter S2 ERIES CIRCUITS  The polarity of the voltage across a resistor is determined by the direction of the current. Current entering a resistor create a drop in voltage with the polarity indicated in Figure (a). Reverse the direction the polarity will reverse, Figure (b) Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 VOLTAGE SOURCE IN SERIES VT = VS1 +VS 2 +VS3 +VSn Where n= 1,2,3,4,n….. Voltage sources in series add algebraically. + IS For example, the total voltage of the sources 9V shown is 27 V + What is the total voltage if one battery is 9V reversed? 9 V + 9V Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Reducing series dc voltage sources to a single source. V1 V1 V2 V V2 VT V3 T V3 By following the direction of conventional flow: - There is a rise in potential across the battery (- to + ) - There is drop in potential across the resistor ( + to - ) Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 R1 VS 680 12V Series circuit Tabulating current, resistance, voltage and power is a R3 useful way to summarize parameters in caosmerpileestecitrhceu2it..2k Continuing with the previous example, parameters listed in the Table. I1= 2.74 mA R1= 0.68 k V1= 1.86 V P1= 5.1 mW I2= 2.74 mA R2= 1.50 k V2= 4.11 V P2= 11.3 mW I3= 2.74 mA R3= 2.20 k V3= 6.03 V P3= 16.5 mW IT= 2.74 mA RT= 4.38 k VS= 12 V PT= 32.9 mW Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 .,5&+2))¶692/7$*(/$: Kirchhoff’s voltage law is generally stated as: The algebraic sum of all the voltages around a closed path is zero. In other words, the sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path. V = 0 or Vs = V1 +V2 +V3 +Vn KVL applies to all circuits, but you must apply it to only one closed path. In a series circuit, this is (of course) the entire circuit. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 KIRCHOFF¶S VOLTAGE LAW The algebraic sum of all the voltages around a closed path is zero. V = 0 +Vs -V1 -V2 = 0 Vs = V1 + V2 Which can be written V as s the sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Example Use Kirchoff¶s voltage law to determine the unknown voltage for the circuit in Fig 4.6 Vs1 Vs2 Figure 4.6 © Copyright 2006 Prentice-Hall Principles of Electric Circuits - Floyd

Chapter 2 R1 VS 680 12V Kirchhoff’s voltage law R3 Notice in the series example given earlier that the sum of the resistor voltages is equal to the source voltage2..2k I1= 2.74 mA R1= 0.68 k V1= 1.86 V P1= 5.1 mW I2= 2.74 mA R2= 1.50 k V2= 4.11 V P2= 11.3 mW I3= 2.74 mA R3= 2.20 k V3= 6.03 V P3= 16.5 mW IT= 2.74 mA RT= 4.38 k VS= 12 V PT= 32.9 mW Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 VOLTAGE DIVISION IN A SERIES CIRCUIT  The voltage across V the resistive elements will divide s as the magnitude of the resistance © Copyright 2006 Prentice-Hall levels.  The greater the value of a resistor in a series circuit, the more of the applied voltage it will capture. Principles of Electric Circuits - Floyd

Chapter 2 VOLTAGE DIVIDER RULE First, determine the total resistance as follows: RT = R1 + R2 Then Is = I1 = I2 = Vs RT Apply Ohm’s law to each resistor: = I1R1 =  Vs R1 = R1 Vs V RT RT s V1 V2 = I2 R2 =  Vs R2 = R2 Vs RT RT The resulting format for V1 and V2 is Vx = Rx Vs = Rx Vs RT RT Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Power in Series Circuits R1 470  Use the voltage divider rule to VS + R2 20 V 330  find V1 and V2. Then find the power in R1 and R2 and PT. Applying the voltage The power dissipated by each divider rule: resistor is: (11.75 V)2 V1 = 20 V  470   = 11.75 V }P1 = 470  = 0.29 W  800   (8.25 V)2 PT = 0.5 W V2 = 20 V  330   = 8.25 V P2 = 330  = 0.21 W  800   Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Circuit Ground A The term “ground” typically means a VS + R1 12 V 5.0 k B common or reference point in the circuit. R2 Voltages that are given with respect to 10 k C ground are shown with a single subscript. For example, VA means the voltage at point A with respect to ground. VB means the voltage at point B with respect to ground. VAB means the voltage between points A and B. What are VA, VB, and VAB for the circuit shown? VA = 12 V VB = 8 V VAB = 4 V Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 RESISTORS IN PARALLEL Resistors that are connected to the same two points/nodes are said to be in parallel. A R1 R2 R3 R4 B Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Schematic representations of three parallel resistors. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 a) Parallel resistors; (b) R1 and R2 are in parallel; (c) R3 is in parallel with the series combination of R1 and R2. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 PARALLEL RESISTORS  For resistors in parallel, the total resistance is determined from (6.1)  Note that the equation is for the reciprocal of RT rather than for RT.  Once the right side of the equation has been determined, it is necessary to divide the result into 1 to determine the total resistance Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 SPECIAL CASE: TWO PARALLEL RESISTORS  A special case: The total resistance of two resistors is the product of the two divided by their sum. (6.5) The equation was developed to reduce the effects of the inverse relationship when determining RT Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Special case for resistance R1 R2 of two parallel resistors The resistance of two parallel resistors can be found by either: RT = 1 1 1 or RT = R1R2 + R1 + R2 R1 R2 What is the total resistance if R1 = 27 k and R2 = 56 k? 18.2 k Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Parallel Circuits Parallel circuits A parallel circuit is identified by the fact that it has more than one current path (branch) connected to a common voltage source. + R1 R2 R3 R4 VS Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Parallel Circuits Parallel circuit rule for voltage Because all components are connected across the same voltage source, the voltage across each is the same. For example, the source voltage is 5.0 V. What will a volt- meter read if it is placed across each of the resistors? +- 5.0 V +- 5.0 V +- 5.0 V +- 5.0 V + + + + VS R1 R2 680 1.5k +5.0V © Copyright 2006 Prentice-Hall Principles of Electric Circuits - Floyd

Chapter 2 Parallel Circuits Voltage is always the same across parallel elements. V1 = V2 = VS The voltage across resistor 1 equals the voltage across resistor 2, and both equal the voltage supplies by the source. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Parallel circuit + R1 R2 R3 VS 680  1.5 k 2.2 k Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a parallel circuit. Continuing with the previous example, complete the parameters listed in the Table. I1= 7.4 mA R1= 0.68 k V1= 5.0 V P1= 36.8 mW I2= 3.3 mA R2= 1.50 k V2= 5.0 V P2= 16.7 mW I3= 2.3 mA R3= 2.20 k V3= 5.0 V P3= 11.4 mW IT=13.0 mA RT= 386  VS= 5.0 V PT= 64.8 mW Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Kirchhoff¶s Current Law Kirchhoff’s current law is generally stated as: The sum of the currents entering a node is equal to the sum of the currents leaving the node. In other words, the algebraic sum of the current at the junction is zero. Notice in the previous example that the current from the source is equal to the sum of the branch currents. I1= 7.4 mA R1= 0.68 k V1= 5.0 V P1= 36.8 mW I2= 3.3 mA R2= 1.50 k V2= 5.0 V P2= 16.7 mW I3= 2.3 mA R3= 2.20 k V3= 5.0 V P3= 11.4 mW IT=13.0 mA RT= 386  VS= 5.0 V PT= 64.8 mW Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 .LUFKKRII¶V&XUUHQW/DZ • The sum of the currents entering a node is equal to the sum of the currents leaving the node.  Iin = Iout I1 + I4 = I2 + I3 4A + 8A = 2A +10A 12A = 12A Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Kirchhoff¶s Current Law • The algebraic sum of the current at the junction/node is zero.  Inode = 0 I1 + I4 - I2 - I3 = 0 4A + 8A - 2A -10A = 0 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Kirchhoff¶s Current Law  Most common application of the law will be at the junction of two or more paths of current.  Determining whether a current is entering or leaving a junction is sometimes the most difficult task. If the current arrow points toward the junction, the current is entering the junction.  If the current arrow points away from the junction, the current is leaving the junction. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Current Divider Rule  The current divider rule (CDR) is used to find the current through a resistor in a parallel circuit. General points:  For two parallel elements of equal value, the current will divide equally.  For parallel elements with different values, the smaller the resistance, the greater the share of input current.  For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistor values. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Current Divider Rule Vs = IT RT x = 1,2,3,....n Vx = Vs where I x Rx = IT RT Ix = IT RT Rx Ix =  RT IT Rx Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Current Divider Rule Ix = RT IT Rx Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Current divider When current enters a junction it divides with current values that are inversely proportional to the resistance values. The most widely used formula for the current divider is the two-resistor equation. For resistors R1 and R2, I1 =  R2  IT and I2 =  R1 R1  IT  R1 + R2   + R2      Notice the subscripts. The resistor in the numerator is not the same as the one for which current is found. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Wheatstone Bridge Wheatstone bridge The Wheatstone bridge consists of four resistive arms forming two voltage dividers and a dc voltage source. The output is taken between the dividers. Frequently, one of the bridge resistors is adjustable. When the bridge is balanced, the output voltage is zero, and the products of resistances in the opposite diagonal arms are equal. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Wheatstone bridge Example: What is the 470  330  value of R2 if the bridge 12 V 270  is balanced? 384  Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Open and Short Circuits  An open circuit can have a potential difference (voltage) across its terminal, but the current is always zero amperes. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 Open and Short Circuits  A short circuit can carry a current of a level determined by the external circuit, but the potential difference (voltage) across its terminals is always zero volts. Insert Fig 6.44 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 2 DMM An important OFF VH multipurpose Hz instrument is the digital multimeter VH (DMM), which can measure A mV H voltage, current, 10 A V and resistance. Many include VV other measurement options. 40 mA COM Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

CHAPTER 3 CABLES

Cable Constructions ❑ A cable consists of three main components:- • Conductor • Insulation • Sheath  External protection is provided by the sheath against mechanical damage, chemical reaction, moisture an so on.

Cable Construction (continue)- 3 • Conductor – An element design to transmit electricity – A single core has one conductor while a three-core has 3 conductors. – A cable may be has single core, 3 core or multiple conductor

Cable Construction (continue)- 4 XLPE PAPER • Insulation – Is a material that reduces or prevents the transmission of electricity – Each conductor is covered by insulation – Insulation is phase to ground and phase to phase

Cable Construction (continue)- 5 • Sheath – Cable protective covering – Metallic or nonmetallic protective covering over the conductor / insulation / shield – External protection is provided by the sheath against mechanical damage, chemical reaction, moisture an so on.

Types of Underground Cables 6 •The identification of the cable are based on the several items : • Insulation • Voltage System • Cable Sizing And Core • Technical Specification Characteristics Of The Cable

Types of Underground Cables (continue)- 7 •Usually the operating voltage decides the types of insulation and cable placed in various categories depending upon the voltage for which they are designed. –Low Voltage Cable (LV)  11kV –High Voltage Cable (HV)  11 kV