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Nodal AnalysisProcedure
1. Count the number of nodes = N
2. Choose one of the nodes to be a reference node (0V) when there is no ground
3. Give the voltage for other nodes to be V1, V2, V3, …
4. Use Kirchoff’s current law on each node to form N-1 equations
5. Solve the equations to find V1, V2, V3, …
1Ω
2Ω
-8A 5Ω-25A
3Ω
4Ω
-3A
V1 V2 V3
0V
132332417
0241436331396
03
213
4
318
VVV
VVVV
VVVV
Equation 1
1Ω
2Ω
-8A 5Ω-25A
3Ω
4Ω
-3A
V1 V2 V3
0V
183321112
0263323181222
01
02
2
323
3
12
VVV
VVVVV
VVVVV
Equation 2
1Ω
2Ω
-8A 5Ω-25A
3Ω
4Ω
-3A
V1 V2 V3
0V
50031921015
0345001535210310
05
0325
4
13
2
23
VVV
VVVVV
VVVVV
Equation 3
Cramer’s Rule (Optional)
50031921015
183321112
132332417
VVV
VVV
VVV
956.0816
780
19105
3112
347
1910500
31118
34132
1
V
576.10816
8628
19105
3112
347
195005
3182
31327
2
V
132.32816
26220
19105
3112
347
500105
18112
13247
3
V
50031921015
183321112
132332417
VVV
VVV
VVV
Supernode
When there is a voltage source in the circuit, direct KCL cannot be used because we do not know the current in the voltage source.
We will use the idea of supernode.
Supernode is the method that combines 2 nodes together when using KCL. It will include the voltage source within the circle when using KCL.
1Ω-8A 5Ω-25A
3Ω
4Ω
-3A
1V
V1 V2 V3
0V
132
1680327280135
02603121500115315180120220
01
02
5
0325
4
133
3
12
VV
VVV
VVVVVV
VVVVVV
Equation 2
supernode
Equation 3
Measure the Resistance ofAmmeter and Voltmeter
Adjust a multimeter to measure volt and use another multimeter to measure its resistance.
Adjust a multimeter to measure amp and use another multimeter to measure its resistance.
Standard Resistor Value
1R0 10R 100R 1K0 10K 100K 1M0 10M
1R2 12R 120R 1K2 12K 120K 1M2 n/a
1R5 15R 150R 1K5 15K 150K 1M5 n/a
1R8 18R 180R 1K8 18K 180K 1M8 n/a
2R2 22R 220R 2K2 22K 220K 2M2 n/a
2R7 27R 270R 2K7 27K 270K 2M7 n/a
3R3 33R 330R 3K3 33K 330K 3M3 n/a
3R9 39R 390R 3K9 39K 390K 3M9 n/a
4R7 47R 470R 4K7 47K 470K 4M7 n/a
5R6 56R 560R 5K6 56K 560K 5M6 n/a
6R8 68R 680R 6K8 68K 680K 6M8 n/a
8R2 82R 820R 8K2 82K 820K 8M2 n/a
E12 -Standard
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