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​12 VR2​5 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 2 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​2 Ω+−V1​20 VR2​4 Ω+−V2​24 VR3​8 Ω+−V3​6 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 20 VR1 = 2 ΩV2 = 24 VR2 = 4 ΩV3 = 6 VR3 = 8 Ω
VA = V
3.Medium
R1​ = 4 ΩR3​ = 8 ΩIR3​+−V1​9 VR2​5 ΩAR4​6 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 4 ΩR2 = 5 ΩR3 = 8 ΩR4 = 6 Ω
IR3 = A
4.Medium
R1​ = 3 ΩIR1​R3​ = 20 Ω+−V1​9 VR2​2 ΩAR4​8 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 3 ΩR2 = 2 ΩR3 = 20 ΩR4 = 8 Ω
IR1 = A
5.Hard
R1​ = 4 ΩR2​ = 3 ΩR4​ = 2 Ω+−V1​15 VR3​30 ΩAR5​2 ΩBIs​0.5 A+−V2​15 V

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

V1 = 15 VIs = 0.5 AV2 = 15 VR1 = 4 ΩR2 = 3 ΩR3 = 30 ΩR4 = 2 ΩR5 = 2 Ω
VA = V
6.Hard
R1​ = 15 ΩR3​ = 10 Ω+−V1​5 VR2​6 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 15 ΩR2 = 6 ΩR3 = 10 ΩR4 = 30 ΩVA = 11 V
Is = A

Answer key

  1. 1. PIs = 38.57 W
  2. 2. VA = 19.14 V
  3. 3. IR3 = −0.8014 A
  4. 4. IR1 = 1.521 A
  5. 5. VA = 10.78 V
  6. 6. Is = 3.344 A

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