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 ΩR2​ = 3 ΩIR2​+−V1​6 VR3​8 ΩA+−V2​15 V

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

V1 = 6 VV2 = 15 VR1 = 5 ΩR2 = 3 ΩR3 = 8 Ω
IR2 = A
2.Easy
R1​ = 8 Ω+−V1​18 VR2​?AIs​3 A

The node voltage at A is measured as VA = 17 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 3 AR1 = 8 ΩVA = 17 V
R2 = Ω
3.Medium
−+Vs​ = 9 VIs​3 AAR1​10 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 = 3 AVs = 9 VR1 = 10 ΩR2 = 20 Ω
VA = V
4.Medium
R1​ = 10 ΩR3​ = 3 Ω+−V1​15 VR2​3 ΩAR4​15 ΩBIs​3 A

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

V1 = 15 VIs = 3 AR1 = 10 ΩR2 = 3 ΩR3 = 3 ΩR4 = 15 Ω
VA = V
5.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​30 VR2​25 ΩAR4​8 ΩB0.25·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.25·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 30 VR1 = 4 ΩR2 = 25 ΩR3 = 6 ΩR4 = 8 Ωg = 0.25 A/V
VA = V
6.Hard
R1​ = 25 ΩIR1​+−Vs​ = 8 V+−V1​18 VR2​3 ΩAR3​5 ΩBIs​2.5 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 = 18 VIs = 2.5 AVs = 8 VR1 = 25 ΩR2 = 3 ΩR3 = 5 Ω
IR1 = A

Answer key

  1. 1. IR2 = −1.861 A
  2. 2. R2 = 5.44 Ω
  3. 3. VA = 17 V
  4. 4. VA = −2.045 V
  5. 5. VA = 34.31 V
  6. 6. IR1 = 0.3837 A

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