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​ = 12 Ω+−V1​10 VR2​5 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 12 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​ = 3 Ω+−V1​6 VR2​?AIs​3 A

The node voltage at A is measured as VA = 5.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 3 AR1 = 3 ΩVA = 5.5 V
R2 = Ω
3.Medium
R1​10 Ω+−V1​6 VR2​3 Ω+−V2​15 VI2​R3​4 Ω+−V3​18 VA

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 = 6 VR1 = 10 ΩV2 = 15 VR2 = 3 ΩV3 = 18 VR3 = 4 Ω
I2 = A
4.Medium
R1​ = 15 ΩIR1​R3​ = 15 Ω+−V1​18 VR2​6 ΩAR4​2 ΩBIs​2.5 A

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

V1 = 18 VIs = 2.5 AR1 = 15 ΩR2 = 6 ΩR3 = 15 ΩR4 = 2 Ω
IR1 = A
5.Hard
R1​ = 10 ΩR2​ = 20 ΩR4​ = 5 Ω+−V1​10 VR3​2 ΩAR5​2 ΩBIs​6 A−+V2​30 V

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

V1 = 10 VIs = 6 AV2 = 30 VR1 = 10 ΩR2 = 20 ΩR3 = 2 ΩR4 = 5 ΩR5 = 2 Ω
VB = V
6.Hard
R1​ = 25 ΩR3​ = 4 Ω+−V1​36 VR2​10 ΩAR4​10 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 = 36 VR1 = 25 ΩR2 = 10 ΩR3 = 4 ΩR4 = 10 ΩVA = 18 V
Is = A

Answer key

  1. 1. PIs = 20 W
  2. 2. R2 = 1.737 Ω
  3. 3. I2 = 0.07317 A
  4. 4. IR1 = 0.9933 A
  5. 5. VB = −15.98 V
  6. 6. Is = 3.312 A

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