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​ = 4 ΩIR1​R2​ = 4 Ω+−V1​24 VR3​10 ΩA+−V2​10 V

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

V1 = 24 VV2 = 10 VR1 = 4 ΩR2 = 4 ΩR3 = 10 Ω
IR1 = A
2.Easy
R1​ = 6 ΩR2​ = 4 ΩIR2​+−V1​20 VR3​5 ΩA+−V2​15 V

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

V1 = 20 VV2 = 15 VR1 = 6 ΩR2 = 4 ΩR3 = 5 Ω
IR2 = A
3.Medium
R1​ = 20 ΩR3​ = 12 Ω+−V1​30 VR2​4 ΩAR4​15 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 20 ΩR2 = 4 ΩR3 = 12 ΩR4 = 15 Ω
VB = V
4.Medium
−+Vs​ = 5 VIs​1 AAR1​6 ΩR2​20 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 AVs = 5 VR1 = 6 ΩR2 = 20 Ω
VA = V
5.Hard
R1​ = 8 ΩIR1​+−Vs​ = 10 V+−V1​24 VR2​3 ΩAR3​4 ΩBIs​1 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the current IR1 through R1 in the direction of the arrow.

V1 = 24 VIs = 1 AVs = 10 VR1 = 8 ΩR2 = 3 ΩR3 = 4 Ω
IR1 = A
6.Hard
R1​ = 15 ΩR3​ = 5 Ω+−V1​9 VR2​2 ΩAR4​10 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 VB (measured from ground).

V1 = 9 VR1 = 15 ΩR2 = 2 ΩR3 = 5 ΩR4 = 10 Ωg = 0.2 A/V
VB = V

Answer key

  1. 1. IR1 = 2.458 A
  2. 2. IR2 = −0.8784 A
  3. 3. VB = 21.43 V
  4. 4. VA = 3.462 V
  5. 5. IR1 = 1.853 A
  6. 6. VB = 1.6 V

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