Circuit Analysis III Section 06
Jan 29, 2016
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