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_R2 through R₂ in the direction of the arrow.

V₁ = 8 VI_s = 2 AR₁ = 10 ΩR₂ = 10 Ω

I_R2 = A

2.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 = 3 ΩV₂ = 20 VR₂ = 8 ΩV₃ = 18 VR₃ = 8 Ω

V_A = V

3.Medium

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

V₁ = 6 VI_s = 1.5 AR₁ = 15 ΩR₂ = 20 ΩR₃ = 2 ΩR₄ = 5 Ω

V_B = V

4.Medium

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

V₁ = 30 VI_s = 3 AR₁ = 2 ΩR₂ = 15 ΩR₃ = 8 ΩR₄ = 2 Ω

P_Is = W

5.Hard

The voltage source Vₛ between A and B has its + terminal at A, so it makes V_A − V_B = Vₛ. Use nodal analysis with a supernode to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 9 VI_s = 3 AV_s = 4 VR₁ = 3 ΩR₂ = 20 ΩR₃ = 4 Ω

I_R1 = A

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.4·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the node voltage V_A (measured from ground).

V₁ = 18 VR₁ = 5 ΩR₂ = 25 ΩR₃ = 8 ΩR₄ = 3 Ωg = 0.4 A/V

V_A = V

Answer key

1. I_R2 = 1.4 A
2. V_A = 11.57 V
3. V_B = 6.193 V
4. P_Is = 28.44 W
5. I_R1 = −0.6842 A
6. V_A = 16.23 V

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