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​ = 12 ΩIR1​+−V1​15 VR2​6 ΩAIs​3 A

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

V1 = 15 VIs = 3 AR1 = 12 ΩR2 = 6 Ω
IR1 = A
2.Easy
R1​ = 5 Ω+−V1​18 VR2​6 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 5 ΩR2 = 6 Ω
PIs = W
3.Medium
−+Vs​ = 5 VIs​4 AAR1​5 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 node voltage VA (measured from ground).

Is = 4 AVs = 5 VR1 = 5 ΩR2 = 2 Ω
VA = V
4.Medium
R1​ = 8 ΩR3​ = 10 Ω+−V1​12 VR2​10 ΩAR4​10 ΩBIs​4 A

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

V1 = 12 VIs = 4 AR1 = 8 ΩR2 = 10 ΩR3 = 10 ΩR4 = 10 Ω
VA = V
5.Hard
R1​ = 2 ΩR2​ = 2 ΩIR2​R4​ = 10 Ω+−V1​24 VR3​12 ΩAR5​30 ΩBIs​1.5 A+−V2​30 V

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

V1 = 24 VIs = 1.5 AV2 = 30 VR1 = 2 ΩR2 = 2 ΩR3 = 12 ΩR4 = 10 ΩR5 = 30 Ω
IR2 = A
6.Hard
R1​ = 2 ΩR3​ = 10 Ω+−V1​24 VR2​12 ΩAR4​20 ΩIR4​B0.05·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 current IR4 through R4 in the direction of the arrow.

V1 = 24 VR1 = 2 ΩR2 = 12 ΩR3 = 10 ΩR4 = 20 Ωg = 0.05 A/V
IR4 = A

Answer key

  1. 1. IR1 = −0.1667 A
  2. 2. PIs = 54 W
  3. 3. VA = 2.143 V
  4. 4. VA = 12.73 V
  5. 5. IR2 = −1.175 A
  6. 6. IR4 = 1.029 A

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