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​5 Ω+−V1​18 VR2​12 Ω+−V2​8 VR3​4 Ω+−V3​12 VA

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

V1 = 18 VR1 = 5 ΩV2 = 8 VR2 = 12 ΩV3 = 12 VR3 = 4 Ω
VA = V
2.Easy
R1​ = 6 Ω+−V1​8 VR2​?AIs​1 A

The node voltage at A is measured as VA = 7 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 1 AR1 = 6 ΩVA = 7 V
R2 = Ω
3.Medium
R1​ = 4 ΩR3​ = 2 ΩIR3​+−V1​6 VR2​4 ΩAR4​2 ΩBIs​2 A

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 6 VIs = 2 AR1 = 4 ΩR2 = 4 ΩR3 = 2 ΩR4 = 2 Ω
IR3 = A
4.Medium
R1​15 Ω+−V1​18 VR2​6 Ω+−V2​9 VI2​R3​3 ΩA

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 = 18 VR1 = 15 ΩV2 = 9 VR2 = 6 ΩR3 = 3 Ω
I2 = A
5.Hard
R1​ = 10 ΩIR1​R2​ = 12 ΩR4​ = 5 Ω+−V1​15 VR3​25 ΩAR5​20 ΩBIs​0.5 A−+V2​5 V

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

V1 = 15 VIs = 0.5 AV2 = 5 VR1 = 10 ΩR2 = 12 ΩR3 = 25 ΩR4 = 5 ΩR5 = 20 Ω
IR1 = A
6.Hard
R1​ = 2 Ω+−Vs​ = 10 V+−V1​9 VR2​15 ΩAR3​10 ΩBIs​1 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 node voltage VB (measured from ground).

V1 = 9 VIs = 1 AVs = 10 VR1 = 2 ΩR2 = 15 ΩR3 = 10 Ω
VB = V

Answer key

  1. 1. VA = 13.63 V
  2. 2. R2 = 6 Ω
  3. 3. IR3 = −0.1667 A
  4. 4. I2 = 0.7059 A
  5. 5. IR1 = 0.821 A
  6. 6. VB = −0.25 V

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