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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
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)
kcl for gaussian surfaces
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
kirchoff s voltage law kvl
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
node voltage

+

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

application of kvl

+

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.
application of kcl

R3

R2

R1

Iin

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

A

G

equivalent resistance

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:
design of analog multimeters

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).
voltmeter

+

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)
voltmeter loading

+

+

+

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,
ammeter

+

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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