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​ = 6 Ω+−V1​18 VR2​8 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 6 ΩR2 = 8 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​8 VR2​?AIs​1 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 1 AR1 = 10 ΩVA = 14.5 V
R2 = Ω
3.Medium
R1​15 Ω+−V1​24 VR2​8 Ω−+V2​15 VI2​R3​3 Ω+−V3​30 VA

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 = 15 VR2 = 8 ΩV3 = 30 VR3 = 3 Ω
I2 = A
4.Medium
R1​ = 5 ΩR3​ = 8 Ω+−V1​10 VR2​5 ΩAR4​15 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 5 ΩR2 = 5 ΩR3 = 8 ΩR4 = 15 Ω
VB = V
5.Hard
R1​ = 5 ΩR2​ = 15 ΩIR2​R4​ = 10 Ω+−V1​18 VR3​15 ΩAR5​2 ΩBIs​4 A+−V2​6 V

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

V1 = 18 VIs = 4 AV2 = 6 VR1 = 5 ΩR2 = 15 ΩR3 = 15 ΩR4 = 10 ΩR5 = 2 Ω
IR2 = A
6.Hard
R1​ = 4 Ω−+Vs​ = 8 V+−V1​10 VR2​12 ΩAR3​3 ΩBIs​0.5 A

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 node voltage VA (measured from ground).

V1 = 10 VIs = 0.5 AVs = 8 VR1 = 4 ΩR2 = 12 ΩR3 = 3 Ω
VA = V

Answer key

  1. 1. VA = 20.57 V
  2. 2. R2 = 41.43 Ω
  3. 3. I2 = −4.19 A
  4. 4. VB = 12.21 V
  5. 5. IR2 = 0.2857 A
  6. 6. VA = 0.5 V

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