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​ = 8 Ω+−V1​15 VR2​?AIs​1 A

The node voltage at A is measured as VA = 19.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 1 AR1 = 8 ΩVA = 19.5 V
R2 = Ω
2.Easy
R1​ = 10 ΩR2​ = 4 Ω+−V1​15 VR3​3 ΩIR3​A+−V2​10 V

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

V1 = 15 VV2 = 10 VR1 = 10 ΩR2 = 4 ΩR3 = 3 Ω
IR3 = A
3.Medium
R1​2 Ω+−V1​12 VR2​6 Ω+−V2​24 VR3​12 Ω+−V3​12 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 12 VR1 = 2 ΩV2 = 24 VR2 = 6 ΩV3 = 12 VR3 = 12 Ω
I3 = A
4.Medium
R1​ = 2 ΩIR1​R3​ = 15 Ω+−V1​24 VR2​4 ΩAR4​2 ΩBIs​3 A

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

V1 = 24 VIs = 3 AR1 = 2 ΩR2 = 4 ΩR3 = 15 ΩR4 = 2 Ω
IR1 = A
5.Hard
R1​ = 25 ΩR2​ = 12 ΩR4​ = 3 Ω+−V1​15 VR3​3 ΩAR5​15 ΩBIs​4 A−+V2​36 V

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

V1 = 15 VIs = 4 AV2 = 36 VR1 = 25 ΩR2 = 12 ΩR3 = 3 ΩR4 = 3 ΩR5 = 15 Ω
VA = V
6.Hard
R1​ = 4 ΩR2​ = 20 ΩIR2​R4​ = 12 Ω+−V1​9 VR3​25 ΩAR5​3 ΩBIs​3 A+−V2​24 V

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

V1 = 9 VIs = 3 AV2 = 24 VR1 = 4 ΩR2 = 20 ΩR3 = 25 ΩR4 = 12 ΩR5 = 3 Ω
IR2 = A

Answer key

  1. 1. R2 = 44.57 Ω
  2. 2. IR3 = 1.951 A
  3. 3. I3 = −0.2222 A
  4. 4. IR1 = 4.364 A
  5. 5. VA = −1.762 V
  6. 6. IR2 = −0.1641 A

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