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 = 18 VR₁ = 8 ΩV₂ = 24 VR₂ = 3 ΩR₃ = 10 Ω

V_A = V

2.Easy

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

V₁ = 10 VV₂ = 12 VR₁ = 5 ΩR₂ = 12 ΩR₃ = 2 Ω

I_R3 = A

3.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₃ in branch 3, flowing up into node A in the direction of the arrow.

V₁ = 10 VR₁ = 3 ΩV₂ = 12 VR₂ = 10 ΩV₃ = 6 VR₃ = 6 Ω

I₃ = 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 node voltage V_B (measured from ground).

I_s = 2.5 AV_s = 4 VR₁ = 6 ΩR₂ = 20 Ω

V_B = V

5.Hard

The current source is adjusted until the node voltage at A is V_A = 4.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 5 VR₁ = 5 ΩR₂ = 3 ΩR₃ = 8 ΩR₄ = 2 ΩV_A = 4.5 V

I_s = A

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.25·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 = 24 VR₁ = 4 ΩR₂ = 3 ΩR₃ = 15 ΩR₄ = 15 Ωg = 0.25 A/V

V_A = V

Answer key

1. V_A = 18.36 V
2. I_R3 = 1.915 A
3. I₃ = −0.537 A
4. V_B = 14.62 V
5. I_s = 9.25 A
6. V_A = 12.2 V

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