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_R3 through R₃ in the direction of the arrow.

V₁ = 20 VV₂ = 8 VR₁ = 12 ΩR₂ = 10 ΩR₃ = 2 Ω

I_R3 = A

2.Easy

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

V₁ = 15 VI_s = 3 AR₁ = 4 ΩR₂ = 6 Ω

I_R2 = A

3.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 = 6 VR₁ = 15 ΩV₂ = 9 VR₂ = 8 ΩV₃ = 9 VR₃ = 8 Ω

I₂ = A

4.Medium

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

V₁ = 15 VI_s = 1.5 AR₁ = 6 ΩR₂ = 5 ΩR₃ = 6 ΩR₄ = 12 Ω

V_A = 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_A (measured from ground).

V₁ = 6 VI_s = 5 AV_s = 5 VR₁ = 25 ΩR₂ = 3 ΩR₃ = 2 Ω

V_A = V

6.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 node voltage V_B (measured from ground).

V₁ = 6 VI_s = 6 AV_s = 6 VR₁ = 3 ΩR₂ = 12 ΩR₃ = 15 Ω

V_B = V

Answer key

1. I_R3 = 1.805 A
2. I_R2 = 2.7 A
3. I₂ = 0.9671 A
4. V_A = 8.289 V
5. V_A = 3.137 V
6. V_B = 11.38 V

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