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​ = 2 Ω+−V1​15 VR2​3 ΩIR2​AIs​1 A

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

V1 = 15 VIs = 1 AR1 = 2 ΩR2 = 3 Ω
IR2 = A
2.Easy
R1​ = 2 ΩR2​ = 10 Ω+−V1​15 VR3​2 ΩA+−V2​18 V

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

V1 = 15 VV2 = 18 VR1 = 2 ΩR2 = 10 ΩR3 = 2 Ω
VA = V
3.Medium
R1​ = 20 ΩIR1​R3​ = 6 Ω+−V1​15 VR2​5 ΩAR4​10 ΩBIs​1 A

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

V1 = 15 VIs = 1 AR1 = 20 ΩR2 = 5 ΩR3 = 6 ΩR4 = 10 Ω
IR1 = A
4.Medium
−+Vs​ = 4 VIs​5 AAR1​10 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 node voltage VA (measured from ground).

Is = 5 AVs = 4 VR1 = 10 ΩR2 = 8 Ω
VA = V
5.Hard
R1​ = 4 ΩR2​ = 25 ΩR4​ = 5 ΩIR4​+−V1​9 VR3​25 ΩAR5​8 ΩBIs​2.5 A+−V2​24 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 9 VIs = 2.5 AV2 = 24 VR1 = 4 ΩR2 = 25 ΩR3 = 25 ΩR4 = 5 ΩR5 = 8 Ω
IR4 = A
6.Hard
R1​ = 5 ΩR3​ = 25 Ω+−V1​9 VR2​4 ΩAR4​15 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 12.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 5 ΩR2 = 4 ΩR3 = 25 ΩR4 = 15 ΩVA = 12.5 V
Is = A

Answer key

  1. 1. IR2 = 3.4 A
  2. 2. VA = 8.455 V
  3. 3. IR1 = 0.53 A
  4. 4. VA = 20 V
  5. 5. IR4 = −0.5947 A
  6. 6. Is = 11.03 A

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