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 = 18 VV₂ = 20 VR₁ = 8 ΩR₂ = 8 ΩR₃ = 6 Ω

V_A = V

2.Easy

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

V₁ = 10 VV₂ = 8 VR₁ = 5 ΩR₂ = 2 ΩR₃ = 10 Ω

I_R2 = A

3.Medium

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

V₁ = 30 VI_s = 4 AR₁ = 8 ΩR₂ = 8 ΩR₃ = 5 ΩR₄ = 4 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 current I_x through the voltage source, from A to B as shown by the arrow.

I_s = 5 AV_s = 10 VR₁ = 12 ΩR₂ = 3 Ω

I_x = A

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 = 9 VI_s = 5 AV_s = 3 VR₁ = 10 ΩR₂ = 30 ΩR₃ = 12 Ω

I_R1 = A

6.Hard

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

V₁ = 24 VI_s = 4 AV₂ = 9 VR₁ = 15 ΩR₂ = 15 ΩR₃ = 12 ΩR₄ = 4 ΩR₅ = 10 Ω

I_R4 = A

Answer key

1. V_A = 11.4 V
2. I_R2 = −0.25 A
3. V_B = 15.69 V
4. I_x = 4.667 A
5. I_R1 = −1.708 A
6. I_R4 = 2.005 A

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