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 Ω+−V1​20 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 2 AR1 = 5 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​ = 5 ΩIR1​+−V1​20 VR2​5 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 5 ΩR2 = 5 Ω
IR1 = A
3.Medium
R1​2 Ω+−V1​15 VR2​10 Ω+−V2​6 VI2​R3​20 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 2 ΩV2 = 6 VR2 = 10 ΩR3 = 20 Ω
I2 = A
4.Medium
R1​ = 12 ΩR3​ = 2 Ω+−V1​15 VR2​4 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 15 VIs = 2.5 AR1 = 12 ΩR2 = 4 ΩR3 = 2 ΩR4 = 5 Ω
PIs = W
5.Hard
R1​ = 30 ΩR3​ = 30 Ω+−V1​6 VR2​30 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 12 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 6 VR1 = 30 ΩR2 = 30 ΩR3 = 30 ΩR4 = 25 ΩVA = 12 V
Is = A
6.Hard
R1​ = 3 ΩR2​ = 12 ΩIR2​R4​ = 12 Ω+−V1​15 VR3​30 ΩAR5​3 ΩBIs​0.5 A+−V2​6 V

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

V1 = 15 VIs = 0.5 AV2 = 6 VR1 = 3 ΩR2 = 12 ΩR3 = 30 ΩR4 = 12 ΩR5 = 3 Ω
IR2 = A

Answer key

  1. 1. R2 = 4.677 Ω
  2. 2. IR1 = 1 A
  3. 3. I2 = −0.6462 A
  4. 4. PIs = 20.31 W
  5. 5. Is = 1.8 A
  6. 6. IR2 = 0.7962 A

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