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​ = 8 Ω+−V1​8 VR2​6 ΩAIs​3 A

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

V1 = 8 VIs = 3 AR1 = 8 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 5 Ω+−V1​8 VR2​8 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 5 ΩR2 = 8 Ω
VA = V
3.Medium
R1​ = 3 ΩR3​ = 20 Ω+−V1​6 VR2​20 ΩAR4​12 ΩBIs​5 A

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

V1 = 6 VIs = 5 AR1 = 3 ΩR2 = 20 ΩR3 = 20 ΩR4 = 12 Ω
VB = V
4.Medium
R1​5 Ω+−V1​6 VR2​4 Ω+−V2​9 VI2​R3​10 Ω−+V3​15 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 = 5 ΩV2 = 9 VR2 = 4 ΩV3 = 15 VR3 = 10 Ω
I2 = A
5.Hard
R1​ = 4 ΩIR1​R2​ = 6 ΩR4​ = 30 Ω+−V1​36 VR3​12 ΩAR5​10 ΩBIs​6 A+−V2​18 V

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

V1 = 36 VIs = 6 AV2 = 18 VR1 = 4 ΩR2 = 6 ΩR3 = 12 ΩR4 = 30 ΩR5 = 10 Ω
IR1 = A
6.Hard
R1​ = 15 ΩR3​ = 3 Ω+−V1​30 VR2​6 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 20.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 30 VR1 = 15 ΩR2 = 6 ΩR3 = 3 ΩR4 = 10 ΩVA = 20.5 V
Is = A

Answer key

  1. 1. PIs = 41.14 W
  2. 2. VA = −1.231 V
  3. 3. VB = 41.01 V
  4. 4. I2 = 1.364 A
  5. 5. IR1 = 1.227 A
  6. 6. Is = 5.668 A

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