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 = 6 VR₁ = 3 ΩV₂ = 15 VR₂ = 12 ΩV₃ = 18 VR₃ = 8 Ω

V_A = V

2.Easy

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

V₁ = 15 VI_s = 1 AR₁ = 10 ΩR₂ = 4 Ω

V_A = V

3.Medium

Use nodal analysis to find the current I_R3 through R₃ in the direction of the arrow.

V₁ = 9 VI_s = 1 AR₁ = 12 ΩR₂ = 12 ΩR₃ = 12 ΩR₄ = 10 Ω

I_R3 = A

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 = 2 AV_s = 3 VR₁ = 6 ΩR₂ = 5 Ω

I_x = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 12.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 15 VR₁ = 8 ΩR₂ = 6 ΩR₃ = 5 ΩR₄ = 10 ΩV_A = 12.5 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 = 10 VI_s = 3 AV_s = 12 VR₁ = 12 ΩR₂ = 25 ΩR₃ = 4 Ω

I_x = A

Answer key

1. V_A = 10.15 V
2. V_A = 1.429 V
3. I_R3 = 0.5179 A
4. I_x = 1.364 A
5. I_s = 3.906 A
6. I_x = −1.424 A

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