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 = 24 VV₂ = 6 VR₁ = 12 ΩR₂ = 2 ΩR₃ = 3 Ω

I_R3 = A

2.Easy

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

V₁ = 18 VV₂ = 24 VR₁ = 4 ΩR₂ = 6 ΩR₃ = 4 Ω

I_R2 = 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_A (measured from ground).

I_s = 1.5 AV_s = 3 VR₁ = 5 ΩR₂ = 8 Ω

V_A = V

4.Medium

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

V₁ = 12 VI_s = 1.5 AR₁ = 15 ΩR₂ = 15 ΩR₃ = 12 ΩR₄ = 3 Ω

V_A = V

5.Hard

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

V₁ = 6 VI_s = 0.5 AV₂ = 24 VR₁ = 10 ΩR₂ = 30 ΩR₃ = 15 ΩR₄ = 4 ΩR₅ = 5 Ω

I_R4 = A

6.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_x through the voltage source, from A to B as shown by the arrow.

V₁ = 5 VI_s = 1.5 AV_s = 12 VR₁ = 20 ΩR₂ = 5 ΩR₃ = 4 Ω

I_x = A

Answer key

1. I_R3 = 1.818 A
2. I_R2 = −1.875 A
3. V_A = 3.462 V
4. V_A = 5.5 V
5. I_R4 = 3.174 A
6. I_x = 0.875 A

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