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​ = 12 ΩIR1​+−V1​10 VR2​5 ΩAIs​1 A

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

V1 = 10 VIs = 1 AR1 = 12 ΩR2 = 5 Ω
IR1 = A
2.Easy
R1​ = 6 ΩR2​ = 12 ΩIR2​+−V1​10 VR3​5 ΩA+−V2​18 V

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 10 VV2 = 18 VR1 = 6 ΩR2 = 12 ΩR3 = 5 Ω
IR2 = A
3.Medium
R1​ = 10 ΩR3​ = 10 Ω+−V1​9 VR2​12 ΩAR4​4 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 10 ΩR2 = 12 ΩR3 = 10 ΩR4 = 4 Ω
PIs = W
4.Medium
R1​ = 8 ΩR3​ = 6 Ω+−V1​30 VR2​20 ΩAR4​15 ΩBIs​2 A

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

V1 = 30 VIs = 2 AR1 = 8 ΩR2 = 20 ΩR3 = 6 ΩR4 = 15 Ω
VA = V
5.Hard
R1​ = 5 ΩR2​ = 12 ΩR4​ = 4 ΩIR4​+−V1​12 VR3​12 ΩAR5​5 ΩBIs​2 A+−V2​18 V

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

V1 = 12 VIs = 2 AV2 = 18 VR1 = 5 ΩR2 = 12 ΩR3 = 12 ΩR4 = 4 ΩR5 = 5 Ω
IR4 = A
6.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​10 VR2​5 ΩAR4​5 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 14 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 4 ΩR2 = 5 ΩR3 = 6 ΩR4 = 5 ΩVA = 14 V
Is = A

Answer key

  1. 1. IR1 = 0.2941 A
  2. 2. IR2 = −0.9136 A
  3. 3. PIs = 31.63 W
  4. 4. VA = 23.26 V
  5. 5. IR4 = −1.076 A
  6. 6. Is = 11.16 A

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