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​ = 8 Ω+−V1​10 VR2​10 ΩAIs​1 A

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

V1 = 10 VIs = 1 AR1 = 8 ΩR2 = 10 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​20 VR2​?AIs​3 A

The node voltage at A is measured as VA = 33 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 3 AR1 = 6 ΩVA = 33 V
R2 = Ω
3.Medium
R1​ = 20 ΩIR1​R3​ = 6 Ω+−V1​6 VR2​8 ΩAR4​12 ΩBIs​2.5 A

Use nodal analysis to find the current IR1 through R1 in the direction of the arrow.

V1 = 6 VIs = 2.5 AR1 = 20 ΩR2 = 8 ΩR3 = 6 ΩR4 = 12 Ω
IR1 = A
4.Medium
−+Vs​ = 8 VIx​Is​1.5 AAR1​6 ΩR2​2 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 = 1.5 AVs = 8 VR1 = 6 ΩR2 = 2 Ω
Ix = A
5.Hard
R1​ = 30 ΩR2​ = 10 ΩR4​ = 4 Ω+−V1​36 VR3​3 ΩAR5​2 ΩBIs​1 A+−V2​9 V

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

V1 = 36 VIs = 1 AV2 = 9 VR1 = 30 ΩR2 = 10 ΩR3 = 3 ΩR4 = 4 ΩR5 = 2 Ω
VB = V
6.Hard
R1​ = 5 ΩR3​ = 8 Ω+−V1​12 VR2​3 ΩAR4​2 ΩIR4​B0.4·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.4·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 12 VR1 = 5 ΩR2 = 3 ΩR3 = 8 ΩR4 = 2 Ωg = 0.4 A/V
IR4 = A

Answer key

  1. 1. PIs = 10 W
  2. 2. R2 = 39.6 Ω
  3. 3. IR1 = −0.1265 A
  4. 4. Ix = 2.125 A
  5. 5. VB = 4.233 V
  6. 6. IR4 = 1.822 A

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