Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsNode, Branch, Loop• Node: point of connection of 2 ormore 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 branchesthat ends in the node where itbegan (closed current path).– A-B-C-D-A+Vin3 Ω2 Ω6 Ω4 ΩIin5 ΩBACDE1 ΩGChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsKirchoff’s Current Law (KCL)• Popular form: the sum of currents entering thenode is equal to the sum of currents leaving thenode (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 currentsalgebraically sum to zero ( add currents enteringthe node and subtract currents leaving the node)Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsKCL for Gaussian Surfaces• Gaussian surface:– closed curve in a plane.– closed surface in 3 dimensions.• The sum of currents entering a Gaussian surface isequal to the sum of currents leaving it.• Drill: #2 p. 59Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsKirchoff’s Voltage Law (KVL)• Popular form: The algebraic sum of the voltagedrops in all branches around a loop is zero (addpositive polarity voltages and subtract negativepolarity voltages).• Drill: #1 p.59• Other forms of KVL:– In traversing a loop, the sum of the voltages having onepolarity is equal to the sum of voltages having theopposite polarity.– For a loop A-B-C-D-A, VAD=VAB+VBC+VCDChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsNode Voltage• Reference node: chosen generally as negative leadof voltage source or tail of current source.• Node voltage: drop from the node to the reference.– VA = VAG– VB = VBG• Consequence of KVL:– VAB= VAG+VGB= VAG-VBG = VA-VB+Vin3 Ω2 Ω6 Ω4 ΩIin5 ΩBACDE1 ΩG = refChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsApplication of KVL• Given the circuit below derive V2 in terms of Vin, R1, R2and R3.+VinR2R3BACR1G++=3R2R1RR2inV2V :RuleDivider VoltageChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsApplication of KCL• Given the circuit below derive V2 in terms of Iin, R1, R2and R3.AGR3econductanc theis R1G ,3G2G1GG2inI2I :RuleDivider Current ii=++=R2R1IinChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsEquivalent Resistance• Equivalent resistance seen at nodes A and B:• Drill: - One or more devices is a source: #28 p. 63 (change Vs polarity)- All devices are resistors: #22 p. 62• Equivalent conductance:ABABeqIVR =+VAB-IABABInterconnectedDevicesABABeqeqVIR1G ==Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsDesign of Analog Multimeters• Multimeter: measures V, I and R.• Digital Multimeter: LED display• Analog multimeter: deflection of needle pointer– Rm: resistance of the movable coil.– Im: current needed to deflect the needle full scale (FS).RmImChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsVoltmeter• Measure voltage:– R1: multiplier resistance added so that the voltmeter can be usedfor a selected voltage range.– Drill: Given that Rm=1,140Ω and Im=50µA, construct a voltmeterhaving a range of 0-10V.• Voltmeter Sensitivity: S = (Rm+R1)/ VFS (Ω/V) R1RmIm+Vmeas-Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsVoltmeter Loading• You have two voltmeters available to measure Vo in thecircuit below. Which one will you choose and why?– Voltmeter1: VFS=10V, Sensitivity=1kΩ/V– Voltmeter1: VFS=10V, Sensitivity=20kΩ/V– Vin=12V, R1=1kΩ, R2=220Ω,+VinR1GR2 R1RmIm+Vmeas-+Vo-Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsAmmeter• Measure current:– Rsh: shunt resistance added so that the ammeter can be used for aselected curent range.– Drill: Given that Rm=105Ω and Im=1mA, construct an ammeterhaving a range of 0-10mA.