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_R1 through R₁ in the direction of the arrow.

V₁ = 24 VI_s = 3 AR₁ = 12 ΩR₂ = 12 Ω

I_R1 = A

2.Easy

Use nodal analysis to find the power P_Is delivered by the current source I_s.

V₁ = 8 VI_s = 2 AR₁ = 5 ΩR₂ = 3 Ω

P_Is = W

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 = 15 VR₂ = 6 ΩV₃ = 18 VR₃ = 5 Ω

I₃ = A

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₂ in branch 2, flowing up into node A in the direction of the arrow.

V₁ = 15 VR₁ = 4 ΩV₂ = 18 VR₂ = 12 ΩV₃ = 12 VR₃ = 6 Ω

I₂ = A

5.Hard

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

V₁ = 6 VI_s = 2 AV₂ = 12 VR₁ = 10 ΩR₂ = 5 ΩR₃ = 6 ΩR₄ = 4 ΩR₅ = 12 Ω

I_R4 = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 7 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 15 VR₁ = 30 ΩR₂ = 4 ΩR₃ = 6 ΩR₄ = 6 ΩV_A = 7 V

I_s = A

Answer key

1. I_R1 = −0.5 A
2. P_Is = 13.5 W
3. I₃ = 2.333 A
4. I₂ = 0.2917 A
5. I_R4 = 0.3511 A
6. I_s = 4.133 A

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