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 Ω+−V1​20 VR2​4 Ω+−V2​12 VR3​10 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 20 VR1 = 12 ΩV2 = 12 VR2 = 4 ΩR3 = 10 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​10 VR2​?AIs​3 A

The node voltage at A is measured as VA = 4.5 V. Use nodal analysis to find the resistance R2.

V1 = 10 VIs = 3 AR1 = 10 ΩVA = 4.5 V
R2 = Ω
3.Medium
R1​ = 20 ΩR3​ = 12 Ω+−V1​30 VR2​2 ΩAR4​3 ΩBIs​3 A

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

V1 = 30 VIs = 3 AR1 = 20 ΩR2 = 2 ΩR3 = 12 ΩR4 = 3 Ω
VA = V
4.Medium
R1​ = 5 ΩIR1​R3​ = 15 Ω+−V1​6 VR2​4 ΩAR4​15 ΩBIs​3 A

Use nodal analysis to find the current IR1 through R1 in the direction of the arrow.

V1 = 6 VIs = 3 AR1 = 5 ΩR2 = 4 ΩR3 = 15 ΩR4 = 15 Ω
IR1 = A
5.Hard
R1​ = 6 Ω+−Vs​ = 12 VIx​+−V1​12 VR2​12 ΩAR3​3 ΩBIs​4 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 12 VIs = 4 AVs = 12 VR1 = 6 ΩR2 = 12 ΩR3 = 3 Ω
Ix = A
6.Hard
R1​ = 2 ΩR2​ = 2 ΩIR2​R4​ = 3 Ω+−V1​5 VR3​3 ΩAR5​25 ΩBIs​5 A−+V2​9 V

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

V1 = 5 VIs = 5 AV2 = 9 VR1 = 2 ΩR2 = 2 ΩR3 = 3 ΩR4 = 3 ΩR5 = 25 Ω
IR2 = A

Answer key

  1. 1. VA = 10.77 V
  2. 2. R2 = 1.268 Ω
  3. 3. VA = 3.405 V
  4. 4. IR1 = 0.08276 A
  5. 5. Ix = −2.286 A
  6. 6. IR2 = −0.401 A

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