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​8 VR2​3 Ω+−V2​18 VR3​12 ΩA

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

V1 = 8 VR1 = 12 ΩV2 = 18 VR2 = 3 ΩR3 = 12 Ω
VA = V
2.Easy
R1​ = 8 ΩR2​ = 5 Ω+−V1​10 VR3​8 ΩIR3​A+−V2​24 V

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 10 VV2 = 24 VR1 = 8 ΩR2 = 5 ΩR3 = 8 Ω
IR3 = A
3.Medium
R1​ = 3 ΩR3​ = 15 Ω+−V1​9 VR2​2 ΩAR4​2 ΩBIs​4 A

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

V1 = 9 VIs = 4 AR1 = 3 ΩR2 = 2 ΩR3 = 15 ΩR4 = 2 Ω
VA = V
4.Medium
−+Vs​ = 4 VIs​4 AAR1​2 ΩR2​15 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 = 4 AVs = 4 VR1 = 2 ΩR2 = 15 Ω
VB = V
5.Hard
R1​ = 20 ΩR2​ = 30 ΩIR2​R4​ = 12 Ω+−V1​15 VR3​12 ΩAR5​6 ΩBIs​5 A+−V2​15 V

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

V1 = 15 VIs = 5 AV2 = 15 VR1 = 20 ΩR2 = 30 ΩR3 = 12 ΩR4 = 12 ΩR5 = 6 Ω
IR2 = A
6.Hard
R1​ = 25 ΩR2​ = 25 ΩR4​ = 25 ΩIR4​+−V1​5 VR3​10 ΩAR5​30 ΩBIs​0.5 A+−V2​5 V

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

V1 = 5 VIs = 0.5 AV2 = 5 VR1 = 25 ΩR2 = 25 ΩR3 = 10 ΩR4 = 25 ΩR5 = 30 Ω
IR4 = A

Answer key

  1. 1. VA = 13.33 V
  2. 2. IR3 = 1.681 A
  3. 3. VA = 3.89 V
  4. 4. VB = 10.59 V
  5. 5. IR2 = −0.4669 A
  6. 6. IR4 = −0.2979 A

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