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 power P_Is delivered by the current source I_s.

V₁ = 6 VI_s = 1 AR₁ = 6 ΩR₂ = 2 Ω

P_Is = W

2.Easy

The node voltage at A is measured as V_A = 32.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 20 VI_s = 2 AR₁ = 8 ΩV_A = 32.5 V

R₂ = Ω

3.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_A (measured from ground).

I_s = 2.5 AV_s = 3 VR₁ = 4 ΩR₂ = 10 Ω

V_A = V

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₂ in branch 2, flowing up into node A in the direction of the arrow.

V₁ = 18 VR₁ = 3 ΩV₂ = 18 VR₂ = 15 ΩV₃ = 15 VR₃ = 6 Ω

I₂ = A

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 = 18 VI_s = 1 AV_s = 8 VR₁ = 8 ΩR₂ = 20 ΩR₃ = 10 Ω

I_x = A

6.Hard

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

V₁ = 10 VI_s = 1.5 AV₂ = 36 VR₁ = 15 ΩR₂ = 8 ΩR₃ = 15 ΩR₄ = 12 ΩR₅ = 8 Ω

I_R4 = A

Answer key

1. P_Is = 3 W
2. R₂ = 74.29 Ω
3. V_A = 6.286 V
4. I₂ = 1.471 A
5. I_x = −0.3273 A
6. I_R4 = 2.64 A

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