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​ = 3 Ω+−V1​15 VR2​?AIs​1 A

The node voltage at A is measured as VA = 7.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 1 AR1 = 3 ΩVA = 7.5 V
R2 = Ω
2.Easy
R1​ = 3 Ω+−V1​15 VR2​6 ΩAIs​3 A

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

V1 = 15 VIs = 3 AR1 = 3 ΩR2 = 6 Ω
PIs = W
3.Medium
R1​ = 5 ΩR3​ = 15 ΩIR3​+−V1​9 VR2​8 ΩAR4​6 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 5 ΩR2 = 8 ΩR3 = 15 ΩR4 = 6 Ω
IR3 = A
4.Medium
R1​12 Ω−+V1​10 VR2​6 Ω+−V2​15 VI2​R3​20 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 = 10 VR1 = 12 ΩV2 = 15 VR2 = 6 ΩV3 = 18 VR3 = 20 Ω
I2 = A
5.Hard
R1​ = 2 ΩR3​ = 2 Ω+−V1​18 VR2​3 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 22 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 18 VR1 = 2 ΩR2 = 3 ΩR3 = 2 ΩR4 = 20 ΩVA = 22 V
Is = A
6.Hard
R1​ = 5 ΩR2​ = 25 ΩR4​ = 30 ΩIR4​+−V1​5 VR3​2 ΩAR5​8 ΩBIs​6 A−+V2​18 V

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

V1 = 5 VIs = 6 AV2 = 18 VR1 = 5 ΩR2 = 25 ΩR3 = 2 ΩR4 = 30 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. R2 = 2.143 Ω
  2. 2. PIs = 48 W
  3. 3. IR3 = −0.2684 A
  4. 4. I2 = 1.074 A
  5. 5. Is = 11.37 A
  6. 6. IR4 = 1.527 A

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