Kirchoff’s Current Law (KCL)KCL for Gaussian SurfacesKirchoff’s Voltage Law (KVL)Node VoltageApplication of KVLApplication of KCLEquivalent ResistanceDesign of Analog MultimetersVoltmeterVoltmeter LoadingAmmeterChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsKirchoff’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 CircuitsKCL 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. 59Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsKirchoff’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, VAD=VAB+VBC+VCDChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsNode 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.–VA = VAG–VB = VBG•Consequence of KVL:–VAB= VAG+VGB = VAG-VBG = VA-VB+Vin3 2 6 4 Iin5 BACDE1 G = refChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsApplication of KVL•Given the circuit below derive V2 in terms of Vin, R1, R2 and R3.+VinR2R3BACR1G3R2R1RR2inV2V :RuleDivider VoltageChapter 2: KCL, KVL and Series-Parallel Resistive CircuitsApplication of KCL•Given the circuit below derive V2 in terms of Iin, R1, R2 and R3.AGR3econductanc theis R1G ,3G2G1GG2inI2I :RuleDivider Current iiR2R1IinChapter 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 used for a selected voltage range.–Drill: Given that Rm=1,140 and Im=50A, construct a voltmeter having a range of 0-10V.•Voltmeter Sensitivity: S = (Rm+R1)/ VFS (V R1RmIm+Vmeas-Chapter 2: KCL, KVL and Series-Parallel Resistive CircuitsVoltmeter Loading •You have two voltmeters available to measure Vo in the circuit below. Which one will you choose and why?–Voltmeter1: VFS=10V, Sensitivity=1k/V–Voltmeter1: VFS=10V, Sensitivity=20k/V–Vin=12V, R1=1k, R2=220, +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 a selected curent range.–Drill: Given that Rm=105 and Im=1mA, construct an ammeter having a range of 0-10mA.
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