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 = 2 AR₁ = 3 ΩR₂ = 5 Ω

P_Is = W

2.Easy

The node voltage at A is measured as V_A = 17.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 8 VI_s = 3 AR₁ = 8 ΩV_A = 17.5 V

R₂ = Ω

3.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₁ in branch 1, flowing up into node A in the direction of the arrow.

V₁ = 9 VR₁ = 5 ΩV₂ = 9 VR₂ = 10 ΩR₃ = 20 Ω

I₁ = A

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₃ in branch 3, flowing up into node A in the direction of the arrow.

V₁ = 10 VR₁ = 10 ΩV₂ = 30 VR₂ = 20 ΩV₃ = 10 VR₃ = 2 Ω

I₃ = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 8.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 10 VR₁ = 2 ΩR₂ = 6 ΩR₃ = 15 ΩR₄ = 30 ΩV_A = 8.5 V

I_s = A

6.Hard

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

V₁ = 9 VI_s = 2.5 AV₂ = 12 VR₁ = 30 ΩR₂ = 3 ΩR₃ = 6 ΩR₄ = 15 ΩR₅ = 5 Ω

I_R4 = A

Answer key

1. P_Is = 15 W
2. R₂ = 9.655 Ω
3. I₁ = 0.2571 A
4. I₃ = −3.077 A
5. I_s = 1.283 A
6. I_R4 = 1.121 A

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