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​6 VR2​?AIs​3 A

The node voltage at A is measured as VA = 8 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 3 AR1 = 2 ΩVA = 8 V
R2 = Ω
2.Easy
R1​ = 8 Ω+−V1​8 VR2​4 ΩIR2​AIs​3 A

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

V1 = 8 VIs = 3 AR1 = 8 ΩR2 = 4 Ω
IR2 = A
3.Medium
R1​12 Ω+−V1​24 VR2​2 Ω+−V2​10 VR3​5 Ω+−V3​30 VI3​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 = 2 ΩV3 = 30 VR3 = 5 Ω
I3 = A
4.Medium
R1​ = 12 ΩR3​ = 2 Ω+−V1​15 VR2​12 ΩAR4​15 ΩBIs​2.5 A

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

V1 = 15 VIs = 2.5 AR1 = 12 ΩR2 = 12 ΩR3 = 2 ΩR4 = 15 Ω
VB = V
5.Hard
R1​ = 3 ΩR3​ = 3 Ω+−V1​36 VR2​5 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 30 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 36 VR1 = 3 ΩR2 = 5 ΩR3 = 3 ΩR4 = 10 ΩVA = 30 V
Is = A
6.Hard
R1​ = 20 ΩR2​ = 2 ΩR4​ = 10 ΩIR4​+−V1​10 VR3​8 ΩAR5​10 ΩBIs​1 A+−V2​12 V

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

V1 = 10 VIs = 1 AV2 = 12 VR1 = 20 ΩR2 = 2 ΩR3 = 8 ΩR4 = 10 ΩR5 = 10 Ω
IR4 = A

Answer key

  1. 1. R2 = 4 Ω
  2. 2. IR2 = 2.667 A
  3. 3. I3 = 2.681 A
  4. 4. VB = 17.93 V
  5. 5. Is = 8.2 A
  6. 6. IR4 = −0.4202 A

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