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​ = 4 Ω+−V1​6 VR2​10 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 4 ΩR2 = 10 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​15 VR2​2 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 6 ΩR2 = 2 Ω
VA = V
3.Medium
R1​ = 5 ΩIR1​R3​ = 3 Ω+−V1​24 VR2​5 ΩAR4​15 ΩBIs​2 A

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

V1 = 24 VIs = 2 AR1 = 5 ΩR2 = 5 ΩR3 = 3 ΩR4 = 15 Ω
IR1 = A
4.Medium
R1​8 Ω+−V1​12 VR2​5 Ω+−V2​10 VI2​R3​3 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 = 12 VR1 = 8 ΩV2 = 10 VR2 = 5 ΩR3 = 3 Ω
I2 = A
5.Hard
R1​ = 2 ΩR2​ = 3 ΩR4​ = 15 ΩIR4​+−V1​12 VR3​25 ΩAR5​20 ΩBIs​6 A+−V2​10 V

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

V1 = 12 VIs = 6 AV2 = 10 VR1 = 2 ΩR2 = 3 ΩR3 = 25 ΩR4 = 15 ΩR5 = 20 Ω
IR4 = A
6.Hard
R1​ = 6 ΩR2​ = 4 ΩR4​ = 12 Ω+−V1​36 VR3​20 ΩAR5​2 ΩBIs​4 A+−V2​9 V

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

V1 = 36 VIs = 4 AV2 = 9 VR1 = 6 ΩR2 = 4 ΩR3 = 20 ΩR4 = 12 ΩR5 = 2 Ω
VB = V

Answer key

  1. 1. PIs = 7.143 W
  2. 2. VA = 5.25 V
  3. 3. IR1 = 1.961 A
  4. 4. I2 = 0.9367 A
  5. 5. IR4 = −1.295 A
  6. 6. VB = 11.39 V

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