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 node voltage V_A (measured from ground).

V₁ = 12 VV₂ = 8 VR₁ = 12 ΩR₂ = 6 ΩR₃ = 6 Ω

V_A = V

2.Easy

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage V_A.

V₁ = 15 VR₁ = 3 ΩV₂ = 12 VR₂ = 5 ΩV₃ = 10 VR₃ = 3 Ω

V_A = V

3.Medium

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

V₁ = 10 VI_s = 2.5 AR₁ = 12 ΩR₂ = 5 ΩR₃ = 10 ΩR₄ = 10 Ω

I_R3 = A

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 = 8 VR₁ = 20 ΩR₂ = 15 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 current I_R1 through R₁ in the direction of the arrow.

V₁ = 10 VI_s = 6 AV_s = 8 VR₁ = 6 ΩR₂ = 12 ΩR₃ = 2 Ω

I_R1 = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 12 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 10 VR₁ = 8 ΩR₂ = 20 ΩR₃ = 30 ΩR₄ = 6 ΩV_A = 12 V

I_s = A

Answer key

1. V_A = 5.6 V
2. V_A = 12.38 V
3. I_R3 = −0.9375 A
4. V_A = 8.286 V
5. I_R1 = 0.8519 A
6. I_s = 7.1 A

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