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 = 20 VV₂ = 10 VR₁ = 10 ΩR₂ = 4 ΩR₃ = 2 Ω

V_A = V

2.Easy

The node voltage at A is measured as V_A = 2.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 6 VI_s = 1 AR₁ = 12 ΩV_A = 2.5 V

R₂ = Ω

3.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 = 15 VR₁ = 3 ΩV₂ = 18 VR₂ = 8 ΩV₃ = 30 VR₃ = 4 Ω

I₂ = A

4.Medium

Use nodal analysis to find the power P_Is delivered by the current source I_s.

V₁ = 30 VI_s = 2 AR₁ = 6 ΩR₂ = 12 ΩR₃ = 12 ΩR₄ = 12 Ω

P_Is = W

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 = 15 VI_s = 5 AV_s = 9 VR₁ = 8 ΩR₂ = 6 ΩR₃ = 10 Ω

I_x = A

6.Hard

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

V₁ = 36 VI_s = 1 AV₂ = 18 VR₁ = 4 ΩR₂ = 15 ΩR₃ = 6 ΩR₄ = 25 ΩR₅ = 8 Ω

I_R1 = A

Answer key

1. V_A = 5.294 V
2. R₂ = 1.935 Ω
3. I₂ = −4.059 A
4. P_Is = 44.57 W
5. I_x = −3.915 A
6. I_R1 = 3.886 A

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