Kirchoff s current law kcl
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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

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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