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 = 1 AR₁ = 3 ΩR₂ = 6 Ω

I_R2 = A

2.Easy

The node voltage at A is measured as V_A = 21.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 10 VI_s = 2 AR₁ = 10 ΩV_A = 21.5 V

R₂ = Ω

3.Medium

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

V₁ = 10 VI_s = 1.5 AR₁ = 8 ΩR₂ = 5 ΩR₃ = 20 ΩR₄ = 2 Ω

I_R3 = 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 = 1 AV_s = 6 VR₁ = 15 ΩR₂ = 20 Ω

V_B = V

5.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 = 24 VR₁ = 8 ΩR₂ = 30 ΩR₃ = 10 ΩR₄ = 2 Ωg = 0.1 A/V

I_R4 = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 24 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 18 VR₁ = 30 ΩR₂ = 30 ΩR₃ = 6 ΩR₄ = 12 ΩV_A = 24 V

I_s = A

Answer key

1. I_R2 = 2.556 A
2. R₂ = 25.29 Ω
3. I_R3 = 0.273 A
4. V_B = 12 V
5. I_R4 = 2.222 A
6. I_s = 3.5 A

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