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

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

V₁ = 24 VR₁ = 8 ΩV₂ = 20 VR₂ = 2 ΩV₃ = 15 VR₃ = 8 Ω

V_A = V

2.Easy

Use nodal analysis to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 8 VI_s = 1 AR₁ = 3 ΩR₂ = 10 Ω

I_R1 = A

3.Medium

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

V₁ = 12 VI_s = 1 AR₁ = 12 ΩR₂ = 8 ΩR₃ = 2 ΩR₄ = 20 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 = 1.5 AV_s = 3 VR₁ = 12 ΩR₂ = 20 Ω

V_B = V

5.Hard

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 current I_R1 through R₁ in the direction of the arrow.

V₁ = 15 VI_s = 2 AV_s = 10 VR₁ = 5 ΩR₂ = 12 ΩR₃ = 6 Ω

I_R1 = A

6.Hard

Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 36 VI_s = 2 AV₂ = 6 VR₁ = 10 ΩR₂ = 10 ΩR₃ = 10 ΩR₄ = 4 ΩR₅ = 4 Ω

I_R4 = A

Answer key

1. V_A = 19.83 V
2. I_R1 = −0.1538 A
3. P_Is = 8.657 W
4. V_B = 13.13 V
5. I_R1 = 1.519 A
6. I_R4 = 0.5735 A

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