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​18 VR2​5 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 8 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​ = 12 Ω+−V1​24 VR2​4 ΩIR2​AIs​3 A

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

V1 = 24 VIs = 3 AR1 = 12 ΩR2 = 4 Ω
IR2 = A
3.Medium
R1​ = 20 ΩR3​ = 4 Ω+−V1​24 VR2​8 ΩAR4​10 ΩBIs​3 A

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

V1 = 24 VIs = 3 AR1 = 20 ΩR2 = 8 ΩR3 = 4 ΩR4 = 10 Ω
VA = V
4.Medium
R1​ = 8 ΩR3​ = 20 ΩIR3​+−V1​24 VR2​10 ΩAR4​12 ΩBIs​3 A

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

V1 = 24 VIs = 3 AR1 = 8 ΩR2 = 10 ΩR3 = 20 ΩR4 = 12 Ω
IR3 = A
5.Hard
R1​ = 25 ΩR3​ = 25 Ω+−V1​10 VR2​30 ΩAR4​15 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 10 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 25 ΩR2 = 30 ΩR3 = 25 ΩR4 = 15 ΩVA = 10 V
Is = A
6.Hard
R1​ = 25 ΩR3​ = 10 Ω+−V1​12 VR2​3 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 13.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 12 VR1 = 25 ΩR2 = 3 ΩR3 = 10 ΩR4 = 25 ΩVA = 13.5 V
Is = A

Answer key

  1. 1. PIs = 48.46 W
  2. 2. IR2 = −0.75 A
  3. 3. VA = 13.57 V
  4. 4. IR3 = −0.622 A
  5. 5. Is = 1.556 A
  6. 6. Is = 6.924 A

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