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​15 VR2​10 Ω+−V2​24 VR3​6 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 15 VR1 = 5 ΩV2 = 24 VR2 = 10 ΩR3 = 6 Ω
VA = V
2.Easy
R1​ = 3 Ω+−V1​6 VR2​5 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 3 ΩR2 = 5 Ω
PIs = W
3.Medium
R1​12 Ω+−V1​10 VR2​10 Ω+−V2​24 VI2​R3​4 Ω+−V3​10 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 = 24 VR2 = 10 ΩV3 = 10 VR3 = 4 Ω
I2 = A
4.Medium
R1​ = 2 ΩR3​ = 3 Ω+−V1​10 VR2​8 ΩAR4​4 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 2 ΩR2 = 8 ΩR3 = 3 ΩR4 = 4 Ω
VB = V
5.Hard
R1​ = 2 ΩR3​ = 20 Ω+−V1​9 VR2​30 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 2 ΩR2 = 30 ΩR3 = 20 ΩR4 = 6 ΩVA = 11 V
Is = A
6.Hard
R1​ = 6 ΩR2​ = 10 ΩR4​ = 8 ΩIR4​+−V1​15 VR3​3 ΩAR5​10 ΩBIs​1 A+−V2​24 V

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

V1 = 15 VIs = 1 AV2 = 24 VR1 = 6 ΩR2 = 10 ΩR3 = 3 ΩR4 = 8 ΩR5 = 10 Ω
IR4 = A

Answer key

  1. 1. VA = 11.57 V
  2. 2. PIs = 28.13 W
  3. 3. I2 = 1.077 A
  4. 4. VB = 6.93 V
  5. 5. Is = 7.756 A
  6. 6. IR4 = −2.02 A

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