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 ΩIR1​+−V1​6 VR2​3 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 5 ΩR2 = 3 Ω
IR1 = A
2.Easy
R1​4 Ω+−V1​15 VR2​8 Ω+−V2​10 VR3​5 Ω+−V3​15 VA

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

V1 = 15 VR1 = 4 ΩV2 = 10 VR2 = 8 ΩV3 = 15 VR3 = 5 Ω
VA = V
3.Medium
R1​ = 15 ΩR3​ = 12 Ω+−V1​30 VR2​4 ΩAR4​12 ΩBIs​1 A

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

V1 = 30 VIs = 1 AR1 = 15 ΩR2 = 4 ΩR3 = 12 ΩR4 = 12 Ω
PIs = W
4.Medium
R1​3 Ω+−V1​24 VR2​5 Ω−+V2​9 VI2​R3​8 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 = 24 VR1 = 3 ΩV2 = 9 VR2 = 5 ΩR3 = 8 Ω
I2 = A
5.Hard
R1​ = 30 ΩR2​ = 5 ΩR4​ = 8 Ω+−V1​36 VR3​20 ΩAR5​25 ΩBIs​3 A+−V2​30 V

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

V1 = 36 VIs = 3 AV2 = 30 VR1 = 30 ΩR2 = 5 ΩR3 = 20 ΩR4 = 8 ΩR5 = 25 Ω
VA = V
6.Hard
R1​ = 15 ΩR3​ = 15 Ω+−V1​5 VR2​15 ΩAR4​3 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 15 ΩR2 = 15 ΩR3 = 15 ΩR4 = 3 ΩVA = 5 V
Is = A

Answer key

  1. 1. IR1 = 0.375 A
  2. 2. VA = 13.91 V
  3. 3. PIs = 9.488 W
  4. 4. I2 = −3.684 A
  5. 5. VA = 28.19 V
  6. 6. Is = 3.667 A

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