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​ = 3 Ω+−V1​10 VR2​?AIs​1 A

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

V1 = 10 VIs = 1 AR1 = 3 ΩVA = 11.5 V
R2 = Ω
2.Easy
R1​10 Ω+−V1​10 VR2​4 Ω+−V2​8 VR3​4 ΩA

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

V1 = 10 VR1 = 10 ΩV2 = 8 VR2 = 4 ΩR3 = 4 Ω
VA = V
3.Medium
R1​ = 15 ΩIR1​R3​ = 15 Ω+−V1​12 VR2​5 ΩAR4​10 ΩBIs​4 A

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

V1 = 12 VIs = 4 AR1 = 15 ΩR2 = 5 ΩR3 = 15 ΩR4 = 10 Ω
IR1 = A
4.Medium
−+Vs​ = 5 VIx​Is​1.5 AAR1​3 ΩR2​2 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = 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.

Is = 1.5 AVs = 5 VR1 = 3 ΩR2 = 2 Ω
Ix = A
5.Hard
R1​ = 6 ΩR2​ = 25 ΩR4​ = 5 Ω+−V1​18 VR3​12 ΩAR5​8 ΩBIs​6 A+−V2​12 V

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

V1 = 18 VIs = 6 AV2 = 12 VR1 = 6 ΩR2 = 25 ΩR3 = 12 ΩR4 = 5 ΩR5 = 8 Ω
VA = V
6.Hard
R1​ = 2 Ω+−Vs​ = 6 VIx​+−V1​9 VR2​6 ΩAR3​5 ΩBIs​3 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 = 9 VIs = 3 AVs = 6 VR1 = 2 ΩR2 = 6 ΩR3 = 5 Ω
Ix = A

Answer key

  1. 1. R2 = 23 Ω
  2. 2. VA = 5 V
  3. 3. IR1 = 0.9739 A
  4. 4. Ix = 1.9 A
  5. 5. VA = 13.73 V
  6. 6. Ix = −2.192 A

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