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​10 VR2​4 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 6 ΩR2 = 4 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​15 VR2​6 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 10 ΩR2 = 6 Ω
PIs = W
3.Medium
−+Vs​ = 10 VIs​1.5 AAR1​8 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 = 1.5 AVs = 10 VR1 = 8 ΩR2 = 8 Ω
VA = V
4.Medium
R1​ = 6 ΩR3​ = 2 ΩIR3​+−V1​6 VR2​2 ΩAR4​3 ΩBIs​1.5 A

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

V1 = 6 VIs = 1.5 AR1 = 6 ΩR2 = 2 ΩR3 = 2 ΩR4 = 3 Ω
IR3 = A
5.Hard
R1​ = 6 ΩR3​ = 3 Ω+−V1​12 VR2​3 ΩAR4​5 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 VA (measured from ground).

V1 = 12 VR1 = 6 ΩR2 = 3 ΩR3 = 3 ΩR4 = 5 Ωg = 0.2 A/V
VA = V
6.Hard
R1​ = 30 ΩR2​ = 15 ΩIR2​R4​ = 3 Ω+−V1​6 VR3​15 ΩAR5​8 ΩBIs​4 A+−V2​24 V

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

V1 = 6 VIs = 4 AV2 = 24 VR1 = 30 ΩR2 = 15 ΩR3 = 15 ΩR4 = 3 ΩR5 = 8 Ω
IR2 = A

Answer key

  1. 1. VA = −0.8 V
  2. 2. PIs = 9.375 W
  3. 3. VA = 1 V
  4. 4. IR3 = −0.4615 A
  5. 5. VA = 4 V
  6. 6. IR2 = −0.2475 A

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