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​15 VR2​6 ΩAIs​3 A

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

V1 = 15 VIs = 3 AR1 = 6 ΩR2 = 6 Ω
VA = V
2.Easy
R1​ = 3 Ω+−V1​18 VR2​2 ΩAIs​1 A

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

V1 = 18 VIs = 1 AR1 = 3 ΩR2 = 2 Ω
PIs = W
3.Medium
R1​ = 20 ΩR3​ = 8 ΩIR3​+−V1​9 VR2​5 ΩAR4​20 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 20 ΩR2 = 5 ΩR3 = 8 ΩR4 = 20 Ω
IR3 = A
4.Medium
−+Vs​ = 8 VIx​Is​3 AAR1​6 ΩR2​4 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 = 3 AVs = 8 VR1 = 6 ΩR2 = 4 Ω
Ix = A
5.Hard
R1​ = 2 ΩR2​ = 2 ΩIR2​R4​ = 20 Ω+−V1​30 VR3​4 ΩAR5​25 ΩBIs​0.5 A−+V2​12 V

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

V1 = 30 VIs = 0.5 AV2 = 12 VR1 = 2 ΩR2 = 2 ΩR3 = 4 ΩR4 = 20 ΩR5 = 25 Ω
IR2 = A
6.Hard
R1​ = 3 ΩR3​ = 4 Ω+−V1​10 VR2​3 ΩAR4​4 ΩB0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 10 VR1 = 3 ΩR2 = 3 ΩR3 = 4 ΩR4 = 4 Ωg = 0.05 A/V
VB = V

Answer key

  1. 1. VA = 16.5 V
  2. 2. PIs = 8.4 W
  3. 3. IR3 = −0.5687 A
  4. 4. Ix = 2.6 A
  5. 5. IR2 = 1.462 A
  6. 6. VB = 2.609 V

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