Nodal analysis worksheet with answers

Free printable Nodal analysis worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

Use nodal analysis to find the node voltage V_A (measured from ground).

V₁ = 6 VI_s = 2 AR₁ = 12 ΩR₂ = 2 Ω

V_A = V

2.Easy

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage V_A.

V₁ = 8 VR₁ = 8 ΩV₂ = 6 VR₂ = 5 ΩV₃ = 10 VR₃ = 2 Ω

V_A = V

3.Medium

Use nodal analysis to find the power P_Is delivered by the current source I_s.

V₁ = 12 VI_s = 2.5 AR₁ = 10 ΩR₂ = 8 ΩR₃ = 10 ΩR₄ = 6 Ω

P_Is = W

4.Medium

The voltage source Vₛ between A and B has its + terminal at B, so it makes V_B − V_A = Vₛ. Use nodal analysis with a supernode to find the node voltage V_B (measured from ground).

I_s = 2 AV_s = 4 VR₁ = 12 ΩR₂ = 4 Ω

V_B = V

5.Hard

The voltage source Vₛ between A and B has its + terminal at A, so it makes V_A − V_B = Vₛ. Use nodal analysis with a supernode to find the current I_x through the voltage source, from A to B as shown by the arrow.

V₁ = 36 VI_s = 5 AV_s = 9 VR₁ = 25 ΩR₂ = 2 ΩR₃ = 6 Ω

I_x = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 17 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 30 VR₁ = 25 ΩR₂ = 15 ΩR₃ = 10 ΩR₄ = 30 ΩV_A = 17 V

I_s = A

Answer key

1. V_A = 4.286 V
2. V_A = 8.727 V
3. P_Is = 30.41 W
4. V_B = 7 V
5. I_x = −4.627 A
6. I_s = 1.384 A

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