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​6 VR2​2 ΩAIs​2 A

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

V1 = 6 VIs = 2 AR1 = 5 ΩR2 = 2 Ω
VA = V
2.Easy
R1​ = 6 Ω+−V1​18 VR2​6 ΩAIs​1 A

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

V1 = 18 VIs = 1 AR1 = 6 ΩR2 = 6 Ω
PIs = W
3.Medium
−+Vs​ = 6 VIs​4 AAR1​6 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 node voltage VA (measured from ground).

Is = 4 AVs = 6 VR1 = 6 ΩR2 = 8 Ω
VA = V
4.Medium
−+Vs​ = 10 VIs​1 AAR1​8 ΩR2​15 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 node voltage VB (measured from ground).

Is = 1 AVs = 10 VR1 = 8 ΩR2 = 15 Ω
VB = V
5.Hard
R1​ = 5 ΩR2​ = 3 ΩIR2​R4​ = 25 Ω+−V1​9 VR3​12 ΩAR5​20 ΩBIs​1 A+−V2​24 V

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

V1 = 9 VIs = 1 AV2 = 24 VR1 = 5 ΩR2 = 3 ΩR3 = 12 ΩR4 = 25 ΩR5 = 20 Ω
IR2 = A
6.Hard
R1​ = 30 ΩR3​ = 30 Ω+−V1​15 VR2​6 ΩAR4​15 ΩB0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 15 VR1 = 30 ΩR2 = 6 ΩR3 = 30 ΩR4 = 15 Ωg = 0.2 A/V
VB = V

Answer key

  1. 1. VA = 4.571 V
  2. 2. PIs = 12 W
  3. 3. VA = 11.14 V
  4. 4. VB = 11.74 V
  5. 5. IR2 = −0.8744 A
  6. 6. VB = 7.5 V

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