Circuit Analysis IIISection 06

Multiple Sources What if more than one source in the circuit?

How to solve for all currents?

Slide 2

KVL and KCL (nodes, loops, planner circuit, voltage drop)

then what?

To solve for all currents and volts in a circuit:

KVL: Kirchhoff’s Voltage Law the algebraic sum of voltages in a loop is zero

KCL: Kirchhoff’s Current Law the algebraic sum of currents into a node is zero

Slide 3

Circuit Analysis

1. count nodes minus one (possible ground)2. mark a current for each branch

name and direction

3. write KCL equations for each node4. count the loops5. write the KVL equations for each loop6. solve for all unknowns

Slide 4

Example

Slide 5

1

0

+ -

+++

-

-

-1 2

Example

Slide 6

1

0

+ -

+++

-

-

-

321: IIIKCL

01245

0565.1:

223

31

III

IIKVL mAI

mAI

mAI

5.116

4.36

9.152

3

2

1

Example

Slide 7

8 branches 8 currents I1..I8 8 equations4 nodes 4 eqs4 loops 4 eqs

Impedance treat all passive components as resistors

but with complex resistances

Electrical Engineering Umm Al-Qura University Slide 8

Impedance What is the impedance of a 10mF capacitor

when operated at 60Hz?

What is the impedance of a 2mH inductor when operated at 60Hz?

Electrical Engineering Umm Al-Qura University Slide 9

25.2651010602 6 j

jwCj

ZC

754.0102602 3 jjjwLZL

Example

Electrical Engineering Umm Al-Qura University Slide 10

Solution

Electrical Engineering Umm Al-Qura University Slide 11

321: IIIKCL

010003.11531

0531000,20110:

223

31

IIjIj

IjIKVL

Simulation Solution

Electrical Engineering Umm Al-Qura University Slide 12

Current Source Voltage Source

Generates constant volt regardless of the load

Current SourceGenerates constant current regardless of the

load

Electrical Engineering Umm Al-Qura University Slide 13

KVL & KCL

Electrical Engineering Umm Al-Qura University Slide 14

Vv 501051

Vv 751552

vx

+

-

21 vvvx

Example

Electrical Engineering Umm Al-Qura University Slide 15

321: IIIKCL

0105

05320:

23

31

ivII

IIKVL

Vv

AI

AI

AI

i 125.48

625.3

3

625.0

3

2

1

AIIS 3: 2

Power Power = rate of energy transfer

measured in Watts (W)

Electrical Engineering Umm Al-Qura University Slide 16

VIP

RIVIP 2

RV

VIP2

Process Check Solve the circuit shown and find the power

consumption of each component

Electrical Engineering Umm Al-Qura University Slide 17

Solution (1)

Electrical Engineering Umm Al-Qura University Slide 18

Akk

I

4001510

10

mWRIP 6.1101010400 3261

21

mWRIP 4.2101510400 3262

22

Solution (2)

Electrical Engineering Umm Al-Qura University Slide 19

Vkk

kV

Vkk

kV

61510

1510

41510

1010

2

1

mWRV

P 6.11010

43

2

1

21

1

mWRV

P 4.21015

63

2

2

22

2

Total Power = 0

Electrical Engineering Umm Al-Qura University Slide 20

mWVIPS 41010400 6

mWPP 421 Total Power = Zero