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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Name: ____________________ Date: ____________

1.Easy

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

V₁ = 24 VI_s = 1 AR₁ = 4 ΩR₂ = 5 Ω

V_A = V

2.Easy

Use nodal analysis to find the current I_R3 through R₃ in the direction of the arrow.

V₁ = 20 VV₂ = 8 VR₁ = 8 ΩR₂ = 8 ΩR₃ = 2 Ω

I_R3 = 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 = 2 AV_s = 12 VR₁ = 20 ΩR₂ = 3 Ω

V_A = V

4.Medium

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

V₁ = 6 VI_s = 5 AR₁ = 2 ΩR₂ = 8 ΩR₃ = 3 ΩR₄ = 3 Ω

V_B = 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 node voltage V_B (measured from ground).

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

V_B = V

6.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 = 12 VR₁ = 25 ΩR₂ = 4 ΩR₃ = 30 ΩR₄ = 3 Ωg = 0.2 A/V

V_B = V

Answer key

1. V_A = 11.11 V
2. I_R3 = 2.333 A
3. V_A = −5.217 V
4. V_B = 10.97 V
5. V_B = 3.913 V
6. V_B = 1.011 V

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