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Kirchoff’s Current Law (KCL)

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)

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Kirchoff’s Current Law (KCL)

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  1. 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)

  2. 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

  3. 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, VAD=VAB+VBC+VCD

  4. + B D E C A 1 W 4 W 3 W 2 W G = ref 5 W 6 W Vin Iin 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. • VA = VAG • VB = VBG • Consequence of KVL: • VAB = VAG+VGB = VAG-VBG = VA-VB

  5. + B A C R2 R1 G R3 Vin Application of KVL • Given the circuit below derive V2 in terms of Vin, R1, R2 and R3.

  6. R3 R2 R1 Iin Application of KCL • Given the circuit below derive V2 in terms of Iin, R1, R2 and R3. A G

  7. IAB A + Interconnected Devices VAB - B Equivalent 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:

  8. Im Rm Design 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).

  9. + Vmeas - R1 Im Rm Voltmeter • Measure voltage: • R1: multiplier resistance added so that the voltmeter can be used for a selected voltage range. • Drill: Given that Rm=1,140W and Im=50mA, construct a voltmeter having a range of 0-10V. • Voltmeter Sensitivity: S = (Rm+R1)/ VFS (W/V)

  10. + + + Vmeas Vo - - R1 R1 R2 Im G Rm Vin Voltmeter Loading • You have two voltmeters available to measure Vo in the circuit below. Which one will you choose and why? • Voltmeter1: VFS=10V, Sensitivity=1kW/V • Voltmeter1: VFS=10V, Sensitivity=20kW/V • Vin=12V, R1=1kW, R2=220W,

  11. + Vmeas - Im Rsh Rm Ammeter • Measure current: • Rsh: shunt resistance added so that the ammeter can be used for a selected curent range. • Drill: Given that Rm=105W and Im=1mA, construct an ammeter having a range of 0-10mA.

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