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 power P_Is delivered by the current source I_s.

V₁ = 20 VI_s = 1 AR₁ = 6 ΩR₂ = 5 Ω

P_Is = W

2.Easy

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

V₁ = 12 VV₂ = 15 VR₁ = 2 ΩR₂ = 5 ΩR₃ = 5 Ω

I_R3 = 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_B (measured from ground).

I_s = 2.5 AV_s = 8 VR₁ = 15 ΩR₂ = 3 Ω

V_B = V

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₁ in branch 1, flowing up into node A in the direction of the arrow.

V₁ = 18 VR₁ = 2 ΩV₂ = 24 VR₂ = 3 ΩR₃ = 5 Ω

I₁ = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 25.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 24 VR₁ = 8 ΩR₂ = 5 ΩR₃ = 4 ΩR₄ = 25 ΩV_A = 25.5 V

I_s = A

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.05·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 15 VR₁ = 10 ΩR₂ = 12 ΩR₃ = 8 ΩR₄ = 5 Ωg = 0.05 A/V

I_R4 = A

Answer key

1. P_Is = 11.82 W
2. I_R3 = 2 A
3. V_B = 7.583 V
4. I₁ = 0.7742 A
5. I_s = 7.153 A
6. I_R4 = 0.6702 A

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