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 = 15 VV₂ = 18 VR₁ = 2 ΩR₂ = 10 ΩR₃ = 3 Ω

V_A = V

2.Easy

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

V₁ = 15 VI_s = 1 AR₁ = 8 ΩR₂ = 8 Ω

P_Is = W

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 = 4 AV_s = 10 VR₁ = 12 ΩR₂ = 6 Ω

V_B = V

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 = 10 VR₁ = 3 ΩV₂ = 10 VR₂ = 5 ΩR₃ = 4 Ω

I₂ = A

5.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.4·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the node voltage V_A (measured from ground).

V₁ = 10 VR₁ = 4 ΩR₂ = 25 ΩR₃ = 12 ΩR₄ = 12 Ωg = 0.4 A/V

V_A = V

6.Hard

Use nodal analysis to find the current I_R2 through R₂ in the direction of the arrow.

V₁ = 24 VI_s = 5 AV₂ = 18 VR₁ = 10 ΩR₂ = 20 ΩR₃ = 2 ΩR₄ = 12 ΩR₅ = 20 Ω

I_R2 = A

Answer key

1. V_A = 9.964 V
2. P_Is = 11.5 W
3. V_B = 19.33 V
4. I₂ = 0.6383 A
5. V_A = 18.99 V
6. I_R2 = −0.7629 A

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