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​ = 2 ΩR2​ = 2 ΩIR2​+−V1​15 VR3​10 ΩA+−V2​20 V

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

V1 = 15 VV2 = 20 VR1 = 2 ΩR2 = 2 ΩR3 = 10 Ω
IR2 = A
2.Easy
R1​ = 3 Ω+−V1​15 VR2​?AIs​1 A

The node voltage at A is measured as VA = 5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 1 AR1 = 3 ΩVA = 5 V
R2 = Ω
3.Medium
R1​ = 4 ΩR3​ = 3 Ω+−V1​18 VR2​10 ΩAR4​12 ΩBIs​1 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 18 VIs = 1 AR1 = 4 ΩR2 = 10 ΩR3 = 3 ΩR4 = 12 Ω
PIs = W
4.Medium
−+Vs​ = 5 VIx​Is​5 AAR1​5 ΩR2​8 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 = 5 AVs = 5 VR1 = 5 ΩR2 = 8 Ω
Ix = A
5.Hard
R1​ = 15 ΩR2​ = 10 ΩR4​ = 8 Ω+−V1​9 VR3​15 ΩAR5​5 ΩBIs​1.5 A+−V2​36 V

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

V1 = 9 VIs = 1.5 AV2 = 36 VR1 = 15 ΩR2 = 10 ΩR3 = 15 ΩR4 = 8 ΩR5 = 5 Ω
VA = V
6.Hard
R1​ = 3 ΩR2​ = 25 ΩR4​ = 10 ΩIR4​+−V1​30 VR3​6 ΩAR5​2 ΩBIs​1 A+−V2​6 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 30 VIs = 1 AV2 = 6 VR1 = 3 ΩR2 = 25 ΩR3 = 6 ΩR4 = 10 ΩR5 = 2 Ω
IR4 = A

Answer key

  1. 1. IR2 = −2.045 A
  2. 2. R2 = 1.154 Ω
  3. 3. PIs = 12.58 W
  4. 4. Ix = 2.308 A
  5. 5. VA = 9.589 V
  6. 6. IR4 = −0.5465 A

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