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_R3 through R₃ in the direction of the arrow.

V₁ = 6 VV₂ = 20 VR₁ = 10 ΩR₂ = 12 ΩR₃ = 4 Ω

I_R3 = A

2.Easy

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

V₁ = 8 VV₂ = 20 VR₁ = 4 ΩR₂ = 8 ΩR₃ = 10 Ω

I_R1 = A

3.Medium

The voltage source Vₛ between A and B has its + terminal at B, so it makes V_B − V_A = Vₛ. Use nodal analysis with a supernode to find the node voltage V_A (measured from ground).

I_s = 1 AV_s = 12 VR₁ = 10 ΩR₂ = 5 Ω

V_A = V

4.Medium

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

V₁ = 30 VI_s = 3 AR₁ = 4 ΩR₂ = 20 ΩR₃ = 20 ΩR₄ = 6 Ω

V_A = V

5.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.05·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 6 VR₁ = 8 ΩR₂ = 15 ΩR₃ = 25 ΩR₄ = 25 Ωg = 0.05 A/V

I_R4 = A

6.Hard

The current source is adjusted until the node voltage at A is V_A = 9.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 5 VR₁ = 8 ΩR₂ = 15 ΩR₃ = 5 ΩR₄ = 8 ΩV_A = 9.5 V

I_s = A

Answer key

1. I_R3 = 1.308 A
2. I_R1 = −0.3684 A
3. V_A = −4.667 V
4. V_A = 24.2 V
5. I_R4 = 0.1808 A
6. I_s = 3.131 A

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