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
R1​ = 12 ΩR2​ = 8 ΩIR2​+−V1​10 VR3​12 ΩA+−V2​20 V

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 10 VV2 = 20 VR1 = 12 ΩR2 = 8 ΩR3 = 12 Ω
IR2 = A
2.Easy
R1​ = 10 Ω+−V1​15 VR2​?AIs​2 A

The node voltage at A is measured as VA = 11.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 2 AR1 = 10 ΩVA = 11.5 V
R2 = Ω
3.Medium
R1​ = 12 ΩR3​ = 6 Ω+−V1​30 VR2​10 ΩAR4​3 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 12 ΩR2 = 10 ΩR3 = 6 ΩR4 = 3 Ω
VA = V
4.Medium
R1​ = 6 ΩR3​ = 20 Ω+−V1​9 VR2​20 ΩAR4​10 ΩBIs​2.5 A

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

V1 = 9 VIs = 2.5 AR1 = 6 ΩR2 = 20 ΩR3 = 20 ΩR4 = 10 Ω
VB = V
5.Hard
R1​ = 30 ΩR3​ = 2 Ω+−V1​15 VR2​4 ΩAR4​5 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 7 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 15 VR1 = 30 ΩR2 = 4 ΩR3 = 2 ΩR4 = 5 ΩVA = 7 V
Is = A
6.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​12 VR2​12 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 16.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 12 VR1 = 4 ΩR2 = 12 ΩR3 = 6 ΩR4 = 10 ΩVA = 16.5 V
Is = A

Answer key

  1. 1. IR2 = −1.071 A
  2. 2. R2 = 4.894 Ω
  3. 3. VA = 11.32 V
  4. 4. VB = −15.78 V
  5. 5. Is = 3.477 A
  6. 6. Is = 5.65 A

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