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​6 Ω+−V1​24 VR2​6 Ω+−V2​8 VR3​10 ΩA

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

V1 = 24 VR1 = 6 ΩV2 = 8 VR2 = 6 ΩR3 = 10 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​15 VR2​5 ΩAIs​2 A

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

V1 = 15 VIs = 2 AR1 = 10 ΩR2 = 5 Ω
VA = V
3.Medium
R1​ = 5 ΩIR1​R3​ = 12 Ω+−V1​12 VR2​20 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 5 ΩR2 = 20 ΩR3 = 12 ΩR4 = 5 Ω
IR1 = A
4.Medium
R1​12 Ω+−V1​24 VR2​10 Ω+−V2​10 VR3​3 ΩI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 24 VR1 = 12 ΩV2 = 10 VR2 = 10 ΩR3 = 3 Ω
I3 = A
5.Hard
R1​ = 15 ΩR3​ = 3 Ω+−V1​36 VR2​5 ΩAR4​15 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 26 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 36 VR1 = 15 ΩR2 = 5 ΩR3 = 3 ΩR4 = 15 ΩVA = 26 V
Is = A
6.Hard
R1​ = 2 ΩR2​ = 15 ΩIR2​R4​ = 10 Ω+−V1​10 VR3​3 ΩAR5​25 ΩBIs​6 A+−V2​24 V

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

V1 = 10 VIs = 6 AV2 = 24 VR1 = 2 ΩR2 = 15 ΩR3 = 3 ΩR4 = 10 ΩR5 = 25 Ω
IR2 = A

Answer key

  1. 1. VA = 12.31 V
  2. 2. VA = 11.67 V
  3. 3. IR1 = 0.3695 A
  4. 4. I3 = −1.935 A
  5. 5. Is = 7.173 A
  6. 6. IR2 = −2.313 A

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