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 current I_R1 through R₁ in the direction of the arrow.

V₁ = 15 VV₂ = 12 VR₁ = 10 ΩR₂ = 2 ΩR₃ = 2 Ω

I_R1 = A

2.Easy

The node voltage at A is measured as V_A = 9.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 20 VI_s = 1 AR₁ = 4 ΩV_A = 9.5 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 = 12 VR₁ = 8 ΩV₂ = 9 VR₂ = 10 ΩV₃ = 24 VR₃ = 15 Ω

I₁ = A

4.Medium

Use nodal analysis to find the node voltage V_B (measured from ground).

V₁ = 15 VI_s = 4 AR₁ = 3 ΩR₂ = 2 ΩR₃ = 10 ΩR₄ = 10 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 node voltage V_B (measured from ground).

V₁ = 12 VI_s = 4 AV_s = 6 VR₁ = 3 ΩR₂ = 6 ΩR₃ = 30 Ω

V_B = V

6.Hard

The current source is adjusted until the node voltage at A is V_A = 16.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 12 VR₁ = 30 ΩR₂ = 25 ΩR₃ = 4 ΩR₄ = 12 ΩV_A = 16.5 V

I_s = A

Answer key

1. I_R1 = 0.8182 A
2. R₂ = 2.621 Ω
3. I₁ = 1.157 A
4. V_B = 23.96 V
5. V_B = 20.63 V
6. I_s = 2.455 A

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