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 Ω+−V1​24 VR2​4 ΩIR2​AIs​2 A

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

V1 = 24 VIs = 2 AR1 = 12 ΩR2 = 4 Ω
IR2 = A
2.Easy
R1​ = 12 Ω+−V1​12 VR2​5 ΩAIs​1 A

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

V1 = 12 VIs = 1 AR1 = 12 ΩR2 = 5 Ω
PIs = W
3.Medium
R1​ = 15 ΩR3​ = 12 Ω+−V1​6 VR2​6 ΩAR4​3 ΩBIs​4 A

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

V1 = 6 VIs = 4 AR1 = 15 ΩR2 = 6 ΩR3 = 12 ΩR4 = 3 Ω
VA = V
4.Medium
R1​8 Ω+−V1​24 VI1​R2​3 Ω+−V2​12 VR3​6 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 24 VR1 = 8 ΩV2 = 12 VR2 = 3 ΩR3 = 6 Ω
I1 = A
5.Hard
R1​ = 8 ΩR3​ = 8 Ω+−V1​6 VR2​12 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 6 VR1 = 8 ΩR2 = 12 ΩR3 = 8 ΩR4 = 20 ΩVA = 11.5 V
Is = A
6.Hard
R1​ = 15 ΩR2​ = 8 ΩR4​ = 12 ΩIR4​+−V1​15 VR3​4 ΩAR5​8 ΩBIs​3 A+−V2​18 V

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

V1 = 15 VIs = 3 AV2 = 18 VR1 = 15 ΩR2 = 8 ΩR3 = 4 ΩR4 = 12 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. IR2 = 3 A
  2. 2. PIs = 7.059 W
  3. 3. VA = 4 V
  4. 4. I1 = 1.6 A
  5. 5. Is = 2.879 A
  6. 6. IR4 = −0.1623 A

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