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 power P_Is delivered by the current source I_s.

V₁ = 6 VI_s = 3 AR₁ = 3 ΩR₂ = 2 Ω

P_Is = W

2.Easy

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage V_A.

V₁ = 8 VR₁ = 2 ΩV₂ = 8 VR₂ = 2 ΩV₃ = 6 VR₃ = 2 Ω

V_A = V

3.Medium

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

V₁ = 18 VI_s = 3 AR₁ = 12 ΩR₂ = 5 ΩR₃ = 5 ΩR₄ = 8 Ω

V_A = V

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 = 10 VR₁ = 5 ΩV₂ = 10 VR₂ = 2 ΩV₃ = 24 VR₃ = 10 Ω

I₂ = A

5.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.2·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 = 6 VR₁ = 25 ΩR₂ = 4 ΩR₃ = 8 ΩR₄ = 20 Ωg = 0.2 A/V

V_B = V

6.Hard

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

V₁ = 15 VI_s = 1 AV₂ = 6 VR₁ = 30 ΩR₂ = 5 ΩR₃ = 8 ΩR₄ = 10 ΩR₅ = 15 Ω

I_R4 = A

Answer key

1. P_Is = 18 W
2. V_A = 7.333 V
3. V_A = −0.9609 V
4. I₂ = −4.625 A
5. V_B = 2.438 V
6. I_R4 = 0.1368 A

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