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 = 10 VR₁ = 8 ΩV₂ = 24 VR₂ = 5 ΩV₃ = 12 VR₃ = 10 Ω

V_A = V

2.Easy

The node voltage at A is measured as V_A = 4 V. Use nodal analysis to find the resistance R₂.

V₁ = 6 VI_s = 2 AR₁ = 4 ΩV_A = 4 V

R₂ = Ω

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 = 12 VR₁ = 8 ΩV₂ = 24 VR₂ = 20 ΩV₃ = 12 VR₃ = 10 Ω

I₃ = A

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 = 10 VR₁ = 5 ΩV₂ = 24 VR₂ = 2 ΩR₃ = 5 Ω

I₁ = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 13 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 15 VR₁ = 2 ΩR₂ = 5 ΩR₃ = 3 ΩR₄ = 2 ΩV_A = 13 V

I_s = A

6.Hard

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

V₁ = 6 VI_s = 3 AV₂ = 24 VR₁ = 20 ΩR₂ = 12 ΩR₃ = 8 ΩR₄ = 5 ΩR₅ = 8 Ω

I_R2 = A

Answer key

1. V_A = 17.06 V
2. R₂ = 1.6 Ω
3. I₃ = 0.8727 A
4. I₁ = −1.111 A
5. I_s = 10.5 A
6. I_R2 = −1.072 A

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