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_R2 through R₂ in the direction of the arrow.

V₁ = 20 VV₂ = 20 VR₁ = 4 ΩR₂ = 5 ΩR₃ = 10 Ω

I_R2 = A

2.Easy

The node voltage at A is measured as V_A = 38 V. Use nodal analysis to find the resistance R₂.

V₁ = 10 VI_s = 3 AR₁ = 12 ΩV_A = 38 V

R₂ = Ω

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 = 1.5 AV_s = 9 VR₁ = 12 ΩR₂ = 10 Ω

I_x = A

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₂ in branch 2, flowing up into node A in the direction of the arrow.

V₁ = 6 VR₁ = 20 ΩV₂ = 9 VR₂ = 5 ΩV₃ = 10 VR₃ = 15 Ω

I₂ = A

5.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 = 10 VI_s = 2.5 AV_s = 8 VR₁ = 5 ΩR₂ = 2 ΩR₃ = 25 Ω

I_x = A

6.Hard

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

V₁ = 12 VI_s = 1 AV₂ = 12 VR₁ = 5 ΩR₂ = 20 ΩR₃ = 5 ΩR₄ = 20 ΩR₅ = 10 Ω

V_A = V

Answer key

1. I_R2 = −0.7273 A
2. R₂ = 57 Ω
3. I_x = 1.227 A
4. I₂ = 0.8947 A
5. I_x = −2.559 A
6. V_A = 6.4 V

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