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​10 VR2​?AIs​3 A

The node voltage at A is measured as VA = 20 V. Use nodal analysis to find the resistance R2.

V1 = 10 VIs = 3 AR1 = 5 ΩVA = 20 V
R2 = Ω
2.Easy
R1​ = 12 Ω+−V1​18 VR2​?AIs​2 A

The node voltage at A is measured as VA = 36.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 2 AR1 = 12 ΩVA = 36.5 V
R2 = Ω
3.Medium
−+Vs​ = 12 VIx​Is​1 AAR1​12 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 = 1 AVs = 12 VR1 = 12 ΩR2 = 8 Ω
Ix = A
4.Medium
R1​ = 2 ΩIR1​R3​ = 2 Ω+−V1​12 VR2​2 ΩAR4​12 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 2 ΩR2 = 2 ΩR3 = 2 ΩR4 = 12 Ω
IR1 = A
5.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​5 VR2​4 ΩAR4​2 ΩIR4​B0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·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 = 5 VR1 = 4 ΩR2 = 4 ΩR3 = 6 ΩR4 = 2 Ωg = 0.5 A/V
IR4 = A
6.Hard
R1​ = 8 ΩR2​ = 20 ΩIR2​R4​ = 20 Ω+−V1​12 VR3​10 ΩAR5​12 ΩBIs​2.5 A+−V2​12 V

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

V1 = 12 VIs = 2.5 AV2 = 12 VR1 = 8 ΩR2 = 20 ΩR3 = 10 ΩR4 = 20 ΩR5 = 12 Ω
IR2 = A

Answer key

  1. 1. R2 = 20 Ω
  2. 2. R2 = 79.64 Ω
  3. 3. Ix = 1.2 A
  4. 4. IR1 = 2.8 A
  5. 5. IR4 = 1.25 A
  6. 6. IR2 = −0.5191 A

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