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

The node voltage at A is measured as V_A = 21.5 V. Use nodal analysis to find the resistance R₂.

V₁ = 24 VI_s = 1 AR₁ = 2 ΩV_A = 21.5 V

R₂ = Ω

2.Easy

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

V₁ = 15 VI_s = 3 AR₁ = 2 ΩR₂ = 8 Ω

V_A = V

3.Medium

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

V₁ = 24 VI_s = 3 AR₁ = 3 ΩR₂ = 5 ΩR₃ = 15 ΩR₄ = 6 Ω

I_R3 = A

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 = 24 VR₁ = 15 ΩV₂ = 9 VR₂ = 6 ΩV₃ = 15 VR₃ = 4 Ω

I₂ = A

5.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 current I_R4 through R₄ in the direction of the arrow.

V₁ = 15 VR₁ = 4 ΩR₂ = 10 ΩR₃ = 15 ΩR₄ = 10 Ωg = 0.4 A/V

I_R4 = A

6.Hard

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

V₁ = 12 VI_s = 3 AV₂ = 5 VR₁ = 15 ΩR₂ = 25 ΩR₃ = 10 ΩR₄ = 10 ΩR₅ = 30 Ω

I_R4 = A

Answer key

1. R₂ = 9.556 Ω
2. V_A = 16.8 V
3. I_R3 = −0.1311 A
4. I₂ = −2.828 A
5. I_R4 = 4.565 A
6. I_R4 = 2.103 A

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