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 = 6 VR₁ = 10 ΩV₂ = 10 VR₂ = 6 ΩR₃ = 10 Ω

V_A = V

2.Easy

Use nodal analysis to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 6 VV₂ = 20 VR₁ = 4 ΩR₂ = 3 ΩR₃ = 8 Ω

I_R1 = A

3.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 = 15 VR₁ = 6 ΩV₂ = 24 VR₂ = 2 ΩV₃ = 9 VR₃ = 6 Ω

I₁ = A

4.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 = 6 VR₁ = 6 ΩV₂ = 18 VR₂ = 3 ΩV₃ = 10 VR₃ = 3 Ω

I₃ = A

5.Hard

Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 9 VI_s = 1 AV₂ = 30 VR₁ = 30 ΩR₂ = 12 ΩR₃ = 12 ΩR₄ = 25 ΩR₅ = 8 Ω

I_R4 = A

6.Hard

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

V₁ = 12 VI_s = 1 AV₂ = 15 VR₁ = 3 ΩR₂ = 5 ΩR₃ = 2 ΩR₄ = 6 ΩR₅ = 4 Ω

V_A = V

Answer key

1. V_A = 6.182 V
2. I_R1 = −1.382 A
3. I₁ = −0.7 A
4. I₃ = −0.8 A
5. I_R4 = −0.7646 A
6. V_A = 5.302 V

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