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 = 12 ΩV₂ = 8 VR₂ = 12 ΩR₃ = 6 Ω

V_A = V

2.Easy

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

V₁ = 15 VV₂ = 8 VR₁ = 12 ΩR₂ = 4 ΩR₃ = 5 Ω

I_R3 = A

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 node voltage V_B (measured from ground).

I_s = 4 AV_s = 5 VR₁ = 8 ΩR₂ = 5 Ω

V_B = V

4.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 node voltage V_A (measured from ground).

I_s = 1.5 AV_s = 12 VR₁ = 8 ΩR₂ = 6 Ω

V_A = V

5.Hard

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

V₁ = 10 VI_s = 5 AV₂ = 36 VR₁ = 2 ΩR₂ = 15 ΩR₃ = 10 ΩR₄ = 2 ΩR₅ = 12 Ω

I_R4 = A

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_A (measured from ground).

V₁ = 30 VI_s = 0.5 AV_s = 9 VR₁ = 2 ΩR₂ = 3 ΩR₃ = 3 Ω

V_A = V

Answer key

1. V_A = 6.5 V
2. I_R3 = 1.219 A
3. V_B = 14.23 V
4. V_A = −1.714 V
5. I_R4 = 0.2642 A
6. V_A = 15.86 V

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