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 current I_R2 through R₂ in the direction of the arrow.

V₁ = 20 VI_s = 2 AR₁ = 2 ΩR₂ = 3 Ω

I_R2 = A

2.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 = 10 ΩV₂ = 20 VR₂ = 8 ΩR₃ = 12 Ω

V_A = V

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 = 2 AV_s = 9 VR₁ = 2 ΩR₂ = 6 Ω

V_A = V

4.Medium

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

V₁ = 12 VI_s = 5 AR₁ = 4 ΩR₂ = 10 ΩR₃ = 4 ΩR₄ = 10 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 node voltage V_A (measured from ground).

V₁ = 6 VI_s = 2.5 AV_s = 15 VR₁ = 12 ΩR₂ = 6 ΩR₃ = 12 Ω

V_A = V

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.1·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 = 5 VR₁ = 15 ΩR₂ = 20 ΩR₃ = 30 ΩR₄ = 5 Ωg = 0.1 A/V

I_R4 = A

Answer key

1. I_R2 = 4.8 A
2. V_A = 14.59 V
3. V_A = 0.75 V
4. V_B = −15.25 V
5. V_A = 12.75 V
6. I_R4 = 0.2909 A

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