Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Node, Branch, Loop Node: point of connection of 2 or more devices –A, B, C, D, E, G –E and D form a super node. Branch: device (current path) connecting 2 adjacent nodes. –AB, BD, CD, DE, EA, AG –ED = short circuit (sc) Loop: connection of branches that ends in the node where it began (closed current path). –A-B-C-D-A + V in 3  2  6  4  I in 5  B A C D E 1  G

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Kirchoff’s Current Law (KCL) Popular form: the sum of currents entering the node is equal to the sum of currents leaving the node (charge cannot accumulate at a node). Drill: –#7(a) p. 60 ( Graph of a circuit) –#14(a) p. 61 (Circuit diagram) Other form of KCL: At a node, all currents algebraically sum to zero ( add currents entering the node and subtract currents leaving the node)

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits KCL for Gaussian Surfaces Gaussian surface: –closed curve in a plane. –closed surface in 3 dimensions. The sum of currents entering a Gaussian surface is equal to the sum of currents leaving it. Drill: #2 p. 59

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Kirchoff’s Voltage Law (KVL) Popular form: The algebraic sum of the voltage drops in all branches around a loop is zero (add positive polarity voltages and subtract negative polarity voltages). Drill: #1 p.59 Other forms of KVL: –In traversing a loop, the sum of the voltages having one polarity is equal to the sum of voltages having the opposite polarity. –For a loop A-B-C-D-A, V AD =V AB +V BC +V CD

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Node Voltage Reference node: chosen generally as negative lead of voltage source or tail of current source. Node voltage: drop from the node to the reference. –V A = V AG –V B = V BG Consequence of KVL: –V AB = V AG +V GB = V AG -V BG = V A -V B + V in 3  2  6  4  I in 5  B A C D E 1  G = ref

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Application of KVL Given the circuit below derive V 2 in terms of V in, R 1, R 2 and R 3. + V in R2 R3R3 B A C R1 G

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Application of KCL Given the circuit below derive V 2 in terms of I in, R 1, R 2 and R 3. A G R3R3 R2R2 R1R1 I in

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Equivalent Resistance Equivalent resistance seen at nodes A and B: Drill: - One or more devices is a source: #28 p. 63 (change V s polarity) - All devices are resistors: #22 p. 62 Equivalent conductance: + V AB - I AB A B Interconnected Devices

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Design of Analog Multimeters Multimeter: measures V, I and R. Digital Multimeter: LED display Analog multimeter: deflection of needle pointer –R m : resistance of the movable coil. –I m : current needed to deflect the needle full scale (FS). RmRm ImIm

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Voltmeter Measure voltage: –R 1 : multiplier resistance added so that the voltmeter can be used for a selected voltage range. –Drill: Given that R m =1,140  and I m =50  A, construct a voltmeter having a range of 0-10V. Voltmeter Sensitivity: S = (R m +R 1 )/ V FS (  V  R 1 RmRm ImIm + V meas -

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Voltmeter Loading You have two voltmeters available to measure V o in the circuit below. Which one will you choose and why? –Voltmeter1: V FS =10V, Sensitivity=1k  /V –Voltmeter1: V FS =10V, Sensitivity=20k  /V –V in =12V, R 1 =1k , R 2 =220 , + V in R1R1 G R2R2 R 1 RmRm ImIm + V meas - + VoVo -

Chapter 2: KCL, KVL and Series-Parallel Resistive Circuits Ammeter Measure current: –R sh : shunt resistance added so that the ammeter can be used for a selected curent range. –Drill: Given that R m =105  and I m =1mA, construct an ammeter having a range of 0-10mA. R sh RmRm ImIm + V meas -