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

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

V₁ = 20 VR₁ = 2 ΩV₂ = 6 VR₂ = 10 ΩV₃ = 10 VR₃ = 5 Ω

V_A = V

2.Easy

Use nodal analysis to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 12 VV₂ = 20 VR₁ = 4 ΩR₂ = 3 ΩR₃ = 3 Ω

I_R1 = 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 = 3 AV_s = 8 VR₁ = 15 ΩR₂ = 8 Ω

V_A = 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 node voltage V_B (measured from ground).

I_s = 1 AV_s = 8 VR₁ = 10 ΩR₂ = 2 Ω

V_B = V

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 = 30 VI_s = 6 AV_s = 6 VR₁ = 6 ΩR₂ = 12 ΩR₃ = 3 Ω

I_x = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 5.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 5 VR₁ = 2 ΩR₂ = 3 ΩR₃ = 10 ΩR₄ = 3 ΩV_A = 5.5 V

I_s = A

Answer key

1. V_A = 15.75 V
2. I_R1 = 0.3636 A
3. V_A = 10.43 V
4. V_B = 3 V
5. I_x = −0.5714 A
6. I_s = 10.86 A

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