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​ = 4 ΩR2​ = 10 ΩIR2​+−V1​6 VR3​6 ΩA+−V2​15 V

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

V1 = 6 VV2 = 15 VR1 = 4 ΩR2 = 10 ΩR3 = 6 Ω
IR2 = A
2.Easy
R1​ = 2 Ω+−V1​18 VR2​12 ΩAIs​2 A

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

V1 = 18 VIs = 2 AR1 = 2 ΩR2 = 12 Ω
PIs = W
3.Medium
R1​ = 8 ΩR3​ = 8 ΩIR3​+−V1​6 VR2​8 ΩAR4​10 ΩBIs​1.5 A

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

V1 = 6 VIs = 1.5 AR1 = 8 ΩR2 = 8 ΩR3 = 8 ΩR4 = 10 Ω
IR3 = A
4.Medium
R1​ = 15 ΩIR1​R3​ = 10 Ω+−V1​18 VR2​3 ΩAR4​2 ΩBIs​1.5 A

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

V1 = 18 VIs = 1.5 AR1 = 15 ΩR2 = 3 ΩR3 = 10 ΩR4 = 2 Ω
IR1 = A
5.Hard
R1​ = 25 ΩR3​ = 4 Ω+−V1​15 VR2​2 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 18 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 15 VR1 = 25 ΩR2 = 2 ΩR3 = 4 ΩR4 = 30 ΩVA = 18 V
Is = A
6.Hard
R1​ = 25 ΩR2​ = 30 ΩR4​ = 6 ΩIR4​+−V1​5 VR3​30 ΩAR5​10 ΩBIs​1 A−+V2​15 V

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

V1 = 5 VIs = 1 AV2 = 15 VR1 = 25 ΩR2 = 30 ΩR3 = 30 ΩR4 = 6 ΩR5 = 10 Ω
IR4 = A

Answer key

  1. 1. IR2 = −0.9194 A
  2. 2. PIs = 37.71 W
  3. 3. IR3 = −0.5455 A
  4. 4. IR1 = 1 A
  5. 5. Is = 10.94 A
  6. 6. IR4 = 0.5216 A

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