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​6 ΩAIs​2 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 15 VIs = 2 AR1 = 2 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 12 Ω+−V1​18 VR2​?AIs​1 A

The node voltage at A is measured as VA = 26.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 1 AR1 = 12 ΩVA = 26.5 V
R2 = Ω
3.Medium
R1​ = 15 ΩR3​ = 5 ΩIR3​+−V1​30 VR2​3 ΩAR4​20 ΩBIs​1.5 A

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

V1 = 30 VIs = 1.5 AR1 = 15 ΩR2 = 3 ΩR3 = 5 ΩR4 = 20 Ω
IR3 = A
4.Medium
R1​ = 12 ΩIR1​R3​ = 8 Ω+−V1​9 VR2​12 ΩAR4​10 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 12 ΩR2 = 12 ΩR3 = 8 ΩR4 = 10 Ω
IR1 = A
5.Hard
R1​ = 12 ΩR2​ = 30 ΩIR2​R4​ = 20 Ω+−V1​5 VR3​2 ΩAR5​15 ΩBIs​2.5 A−+V2​12 V

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

V1 = 5 VIs = 2.5 AV2 = 12 VR1 = 12 ΩR2 = 30 ΩR3 = 2 ΩR4 = 20 ΩR5 = 15 Ω
IR2 = A
6.Hard
R1​ = 6 ΩR2​ = 2 ΩR4​ = 15 Ω+−V1​9 VR3​3 ΩAR5​25 ΩBIs​3 A+−V2​12 V

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

V1 = 9 VIs = 3 AV2 = 12 VR1 = 6 ΩR2 = 2 ΩR3 = 3 ΩR4 = 15 ΩR5 = 25 Ω
VA = V

Answer key

  1. 1. PIs = 28.5 W
  2. 2. R2 = 90.86 Ω
  3. 3. IR3 = −0.9091 A
  4. 4. IR1 = 0.05208 A
  5. 5. IR2 = −0.3865 A
  6. 6. VA = 7.879 V

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