- 2068 Shrawan · 8 marks
Nodal analysis currents in all resistors
Short answer
Node voltages: V_A = 32 V, V_B = 17.6 V, V_C = 13.93 V. Resistor currents: 16.0 A (2 Ω to ground), 7.20 A (A–B), 1.81 A (10 Ω A–C), 3.52 A (5 Ω), 3.68 A (1 Ω B–C), 3.48 A (4 Ω).
Using Nodal Analysis method to find the current in individual resistors of the circuit shown below. [Figure: 25 A current source on the left; 2 Ω shunt; 2 Ω and 1 Ω in series along the middle of the top with a 10 Ω resistor bypass above; 5 Ω shunt; 4 Ω shunt; 2 A current source on the right pointing down.]
Reading the figure
The source on the left is 25 A, as stated in the question. The bottom rail is the reference (0 V).
- Node A: 25 A source (into A), 2 Ω to ground, 2 Ω to node B, 10 Ω (top bypass) to node C.
- Node B: 5 Ω to ground, 1 Ω to node C.
- Node C: 4 Ω to ground, 2 A source taking current out of C (arrow down).
+--------[10 Ω]--------------+
| |
A ---[2 Ω]--- B ---[1 Ω]--- C |
| | | | |
25A [2] [5] [4] (2A)
| | | | |
+--+-----------+-------------+------+
Nodal equations (currents leaving each node)
Node A: V_A/2 + (V_A − V_B)/2 + (V_A − V_C)/10 = 25 Node B: (V_B − V_A)/2 + V_B/5 + (V_B − V_C)/1 = 0 Node C: (V_C − V_A)/10 + (V_C − V_B)/1 + V_C/4 + 2 = 0
Multiplying through (by 10, 10 and 20):
- 11 V_A − 5 V_B − V_C = 250
- −5 V_A + 17 V_B − 10 V_C = 0
- −2 V_A − 20 V_B + 27 V_C = −40
Solving (by Cramer's rule or elimination): V_A = 32.00 V, V_B = 17.60 V, V_C = 13.93 V
Current in each resistor
| Resistor | Voltage | Current |
|---|---|---|
| 2 Ω (A to ground) | 32.00 V | 16.00 A |
| 2 Ω (A to B) | 14.39 V | 7.20 A (A to B) |
| 10 Ω (A to C) | 18.07 V | 1.81 A (A to C) |
| 5 Ω (B to ground) | 17.60 V | 3.52 A |
| 1 Ω (B to C) | 3.68 V | 3.68 A (B to C) |
| 4 Ω (C to ground) | 13.93 V | 3.48 A |
KCL check: at A, 16.00 + 7.20 + 1.81 = 25.0 A. At B, 7.20 = 3.52 + 3.68. At C, 1.81 + 3.68 = 3.48 + 2 (= 5.49 A).
Answer: 16.0 A, 7.20 A, 1.81 A, 3.52 A, 3.68 A and 3.48 A as tabulated.
(If the scan's source value is actually 28 A, the same equations give V_A = 36 V, V_B = 20 V, V_C = 16 V and currents 18, 8, 2, 4, 4 and 4 A.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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