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​ = 5 ΩIR1​+−V1​6 VR2​3 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 5 ΩR2 = 3 Ω
IR1 = A
2.Easy
R1​ = 2 Ω+−V1​10 VR2​?AIs​3 A

The node voltage at A is measured as VA = 9 V. Use nodal analysis to find the resistance R2.

V1 = 10 VIs = 3 AR1 = 2 ΩVA = 9 V
R2 = Ω
3.Medium
R1​ = 2 ΩR3​ = 20 ΩIR3​+−V1​9 VR2​8 ΩAR4​12 ΩBIs​4 A

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

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

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

V1 = 10 VIs = 3 AR1 = 2 ΩR2 = 10 ΩR3 = 3 ΩR4 = 8 Ω
PIs = W
5.Hard
R1​ = 8 ΩR2​ = 15 ΩR4​ = 4 ΩIR4​+−V1​9 VR3​4 ΩAR5​8 ΩBIs​1.5 A+−V2​24 V

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

V1 = 9 VIs = 1.5 AV2 = 24 VR1 = 8 ΩR2 = 15 ΩR3 = 4 ΩR4 = 4 ΩR5 = 8 Ω
IR4 = A
6.Hard
R1​ = 6 ΩR2​ = 5 ΩR4​ = 10 Ω+−V1​18 VR3​3 ΩAR5​3 ΩBIs​6 A−+V2​10 V

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

V1 = 18 VIs = 6 AV2 = 10 VR1 = 6 ΩR2 = 5 ΩR3 = 3 ΩR4 = 10 ΩR5 = 3 Ω
VA = V

Answer key

  1. 1. IR1 = −0.375 A
  2. 2. R2 = 2.571 Ω
  3. 3. IR3 = 1.643 A
  4. 4. PIs = 42.32 W
  5. 5. IR4 = −1.557 A
  6. 6. VA = 7.19 V

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