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 = 2 ΩV₂ = 8 VR₂ = 8 ΩR₃ = 3 Ω

V_A = V

2.Easy

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

V₁ = 6 VV₂ = 10 VR₁ = 2 ΩR₂ = 4 ΩR₃ = 3 Ω

I_R2 = A

3.Medium

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

V₁ = 9 VI_s = 1 AR₁ = 20 ΩR₂ = 4 ΩR₃ = 20 ΩR₄ = 20 Ω

I_R1 = 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 = 18 VR₁ = 2 ΩV₂ = 12 VR₂ = 10 ΩV₃ = 6 VR₃ = 4 Ω

I₃ = A

5.Hard

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

V₁ = 9 VI_s = 1 AV₂ = 18 VR₁ = 12 ΩR₂ = 25 ΩR₃ = 30 ΩR₄ = 12 ΩR₅ = 3 Ω

V_A = V

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.5·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the node voltage V_B (measured from ground).

V₁ = 24 VR₁ = 15 ΩR₂ = 2 ΩR₃ = 8 ΩR₄ = 2 Ωg = 0.5 A/V

V_B = V

Answer key

1. V_A = 4.174 V
2. I_R2 = −1.231 A
3. I_R1 = 0.3038 A
4. I₃ = −1.235 A
5. V_A = 6.326 V
6. V_B = 2.824 V

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