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 = 8 VI_s = 2 AR₁ = 5 ΩR₂ = 3 Ω

P_Is = W

2.Easy

Use nodal analysis to find the current I_R2 through R₂ in the direction of the arrow.

V₁ = 8 VV₂ = 20 VR₁ = 10 ΩR₂ = 8 ΩR₃ = 5 Ω

I_R2 = A

3.Medium

Use nodal analysis to find the current I_R3 through R₃ in the direction of the arrow.

V₁ = 9 VI_s = 1 AR₁ = 2 ΩR₂ = 20 ΩR₃ = 5 ΩR₄ = 20 Ω

I_R3 = A

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 = 24 VR₁ = 2 ΩV₂ = 15 VR₂ = 10 ΩV₃ = 24 VR₃ = 10 Ω

I₂ = A

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_x through the voltage source, from A to B as shown by the arrow.

V₁ = 10 VI_s = 4 AV_s = 12 VR₁ = 6 ΩR₂ = 6 ΩR₃ = 25 Ω

I_x = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 6.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 24 VR₁ = 8 ΩR₂ = 3 ΩR₃ = 20 ΩR₄ = 25 ΩV_A = 6.5 V

I_s = A

Answer key

1. P_Is = 13.5 W
2. I_R2 = −1.529 A
3. I_R3 = 1.051 A
4. I₂ = −3.343 A
5. I_x = −2.964 A
6. I_s = 0.2225 A

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