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 = 15 VI_s = 1 AR₁ = 8 ΩR₂ = 4 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 = 10 VR₁ = 2 ΩR₂ = 8 ΩR₃ = 12 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 current I_x through the voltage source, from A to B as shown by the arrow.

I_s = 3 AV_s = 12 VR₁ = 6 ΩR₂ = 8 Ω

I_x = A

4.Medium

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

V₁ = 24 VI_s = 4 AR₁ = 2 ΩR₂ = 6 ΩR₃ = 6 ΩR₄ = 5 Ω

V_B = V

5.Hard

The current source is adjusted until the node voltage at A is V_A = 13.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 24 VR₁ = 15 ΩR₂ = 6 ΩR₃ = 3 ΩR₄ = 2 ΩV_A = 13.5 V

I_s = 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 current I_x through the voltage source, from A to B as shown by the arrow.

V₁ = 6 VI_s = 4 AV_s = 6 VR₁ = 20 ΩR₂ = 5 ΩR₃ = 3 Ω

I_x = A

Answer key

1. V_A = 7.667 V
2. I_R2 = −0.1471 A
3. I_x = 2.143 A
4. V_B = 19.2 V
5. I_s = 10.62 A
6. I_x = −2.4 A

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