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 Ω+−V1​15 VR2​3 Ω+−V2​8 VR3​12 Ω+−V3​10 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 15 VR1 = 12 ΩV2 = 8 VR2 = 3 ΩV3 = 10 VR3 = 12 Ω
VA = V
2.Easy
R1​ = 2 ΩR2​ = 4 ΩIR2​+−V1​12 VR3​3 ΩA+−V2​12 V

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

V1 = 12 VV2 = 12 VR1 = 2 ΩR2 = 4 ΩR3 = 3 Ω
IR2 = A
3.Medium
R1​ = 10 ΩIR1​R3​ = 4 Ω+−V1​15 VR2​12 ΩAR4​12 ΩBIs​1 A

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

V1 = 15 VIs = 1 AR1 = 10 ΩR2 = 12 ΩR3 = 4 ΩR4 = 12 Ω
IR1 = A
4.Medium
−+Vs​ = 6 VIs​1.5 AAR1​12 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 VB (measured from ground).

Is = 1.5 AVs = 6 VR1 = 12 ΩR2 = 20 Ω
VB = V
5.Hard
R1​ = 6 ΩR2​ = 25 ΩR4​ = 8 Ω+−V1​15 VR3​6 ΩAR5​25 ΩBIs​4 A+−V2​15 V

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

V1 = 15 VIs = 4 AV2 = 15 VR1 = 6 ΩR2 = 25 ΩR3 = 6 ΩR4 = 8 ΩR5 = 25 Ω
VA = V
6.Hard
R1​ = 2 ΩR3​ = 4 Ω+−V1​24 VR2​6 ΩAR4​3 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 19 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 2 ΩR2 = 6 ΩR3 = 4 ΩR4 = 3 ΩVA = 19 V
Is = A

Answer key

  1. 1. VA = 9.5 V
  2. 2. IR2 = −0.9231 A
  3. 3. IR1 = 1.195 A
  4. 4. VB = 15 V
  5. 5. VA = 9.976 V
  6. 6. Is = 7.889 A

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