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 = 18 VR₁ = 4 ΩV₂ = 12 VR₂ = 6 ΩV₃ = 10 VR₃ = 2 Ω

V_A = V

2.Easy

The node voltage at A is measured as V_A = 6 V. Use nodal analysis to find the resistance R₂.

V₁ = 8 VI_s = 3 AR₁ = 4 ΩV_A = 6 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 current I_x through the voltage source, from A to B as shown by the arrow.

I_s = 5 AV_s = 12 VR₁ = 2 ΩR₂ = 3 Ω

I_x = A

4.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 = 24 VR₁ = 8 ΩV₂ = 30 VR₂ = 5 ΩV₃ = 6 VR₃ = 20 Ω

I₁ = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 9 VR₁ = 5 ΩR₂ = 4 ΩR₃ = 3 ΩR₄ = 5 ΩV_A = 5 V

I_s = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 24 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 36 VR₁ = 4 ΩR₂ = 5 ΩR₃ = 6 ΩR₄ = 20 ΩV_A = 24 V

I_s = A

Answer key

1. V_A = 12.55 V
2. R₂ = 1.714 Ω
3. I_x = 4.4 A
4. I₁ = 3.9 A
5. I_s = 1.72 A
6. I_s = 3.54 A

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