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​ = 10 ΩR2​ = 8 ΩIR2​+−V1​8 VR3​5 ΩA+−V2​12 V

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

V1 = 8 VV2 = 12 VR1 = 10 ΩR2 = 8 ΩR3 = 5 Ω
IR2 = A
2.Easy
R1​ = 6 Ω+−V1​18 VR2​4 ΩAIs​1 A

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

V1 = 18 VIs = 1 AR1 = 6 ΩR2 = 4 Ω
PIs = W
3.Medium
R1​ = 15 ΩR3​ = 6 Ω+−V1​12 VR2​12 ΩAR4​8 ΩBIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 15 ΩR2 = 12 ΩR3 = 6 ΩR4 = 8 Ω
VA = V
4.Medium
R1​ = 6 ΩIR1​R3​ = 6 Ω+−V1​12 VR2​15 ΩAR4​8 ΩBIs​4 A

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

V1 = 12 VIs = 4 AR1 = 6 ΩR2 = 15 ΩR3 = 6 ΩR4 = 8 Ω
IR1 = A
5.Hard
R1​ = 15 ΩR3​ = 20 Ω+−V1​24 VR2​25 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 29 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 15 ΩR2 = 25 ΩR3 = 20 ΩR4 = 20 ΩVA = 29 V
Is = A
6.Hard
R1​ = 2 ΩR2​ = 2 ΩR4​ = 6 ΩIR4​+−V1​10 VR3​6 ΩAR5​8 ΩBIs​2 A−+V2​5 V

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

V1 = 10 VIs = 2 AV2 = 5 VR1 = 2 ΩR2 = 2 ΩR3 = 6 ΩR4 = 6 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. IR2 = −0.8235 A
  2. 2. PIs = 9.6 W
  3. 3. VA = 7.484 V
  4. 4. IR1 = −0.3438 A
  5. 5. Is = 4.437 A
  6. 6. IR4 = 1.789 A

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