# Kirchoff’s Current Law (KCL) - PowerPoint PPT Presentation

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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)

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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)

• 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

• 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)

• 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

+

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

+

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.

R3

R2

R1

Iin

### Application of KCL

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

A

G

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:

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).

+

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)

+

+

+

Vmeas

Vo

-

-

R1

R1

R2

Im

G

Rm

Vin

• 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,

+

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.