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​15 VR2​3 Ω+−V2​24 VR3​12 ΩA

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

V1 = 15 VR1 = 12 ΩV2 = 24 VR2 = 3 ΩR3 = 12 Ω
VA = V
2.Easy
R1​ = 2 Ω+−V1​24 VR2​?AIs​1 A

The node voltage at A is measured as VA = 23.5 V. Use nodal analysis to find the resistance R2.

V1 = 24 VIs = 1 AR1 = 2 ΩVA = 23.5 V
R2 = Ω
3.Medium
R1​ = 20 ΩR3​ = 8 ΩIR3​+−V1​15 VR2​20 ΩAR4​2 ΩBIs​1.5 A

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

V1 = 15 VIs = 1.5 AR1 = 20 ΩR2 = 20 ΩR3 = 8 ΩR4 = 2 Ω
IR3 = A
4.Medium
R1​ = 2 ΩR3​ = 10 Ω+−V1​9 VR2​15 ΩAR4​8 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 2 ΩR2 = 15 ΩR3 = 10 ΩR4 = 8 Ω
VA = V
5.Hard
R1​ = 10 ΩR2​ = 15 ΩR4​ = 25 ΩIR4​+−V1​12 VR3​5 ΩAR5​2 ΩBIs​4 A−+V2​18 V

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

V1 = 12 VIs = 4 AV2 = 18 VR1 = 10 ΩR2 = 15 ΩR3 = 5 ΩR4 = 25 ΩR5 = 2 Ω
IR4 = A
6.Hard
R1​ = 8 ΩR2​ = 5 ΩR4​ = 25 Ω+−V1​30 VR3​2 ΩAR5​30 ΩBIs​4 A−+V2​5 V

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

V1 = 30 VIs = 4 AV2 = 5 VR1 = 8 ΩR2 = 5 ΩR3 = 2 ΩR4 = 25 ΩR5 = 30 Ω
VB = V

Answer key

  1. 1. VA = 18.5 V
  2. 2. R2 = 18.8 Ω
  3. 3. IR3 = 0.525 A
  4. 4. VA = 7.946 V
  5. 5. IR4 = 0.9554 A
  6. 6. VB = 20.94 V

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