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​ = 2 Ω+−V1​24 VR2​6 ΩAIs​1 A

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

V1 = 24 VIs = 1 AR1 = 2 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 6 ΩIR1​R2​ = 3 Ω+−V1​6 VR3​5 ΩA+−V2​12 V

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

V1 = 6 VV2 = 12 VR1 = 6 ΩR2 = 3 ΩR3 = 5 Ω
IR1 = A
3.Medium
R1​ = 5 ΩR3​ = 5 Ω+−V1​30 VR2​10 ΩAR4​5 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 5 ΩR2 = 10 ΩR3 = 5 ΩR4 = 5 Ω
VA = V
4.Medium
R1​ = 3 ΩR3​ = 20 ΩIR3​+−V1​18 VR2​12 ΩAR4​8 ΩBIs​1 A

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

V1 = 18 VIs = 1 AR1 = 3 ΩR2 = 12 ΩR3 = 20 ΩR4 = 8 Ω
IR3 = A
5.Hard
R1​ = 3 ΩR2​ = 20 ΩR4​ = 2 Ω+−V1​9 VR3​15 ΩAR5​12 ΩBIs​2.5 A+−V2​6 V

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

V1 = 9 VIs = 2.5 AV2 = 6 VR1 = 3 ΩR2 = 20 ΩR3 = 15 ΩR4 = 2 ΩR5 = 12 Ω
VB = V
6.Hard
R1​ = 12 ΩR2​ = 30 ΩR4​ = 25 ΩIR4​+−V1​30 VR3​15 ΩAR5​15 ΩBIs​1 A+−V2​30 V

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

V1 = 30 VIs = 1 AV2 = 30 VR1 = 12 ΩR2 = 30 ΩR3 = 15 ΩR4 = 25 ΩR5 = 15 Ω
IR4 = A

Answer key

  1. 1. PIs = 19.5 W
  2. 2. IR1 = −0.1905 A
  3. 3. VA = 10 V
  4. 4. IR3 = 0.7368 A
  5. 5. VB = 1.327 V
  6. 6. IR4 = −0.4072 A

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