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​8 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 2 AR1 = 12 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​5 Ω+−V1​6 VR2​3 Ω+−V2​24 VR3​2 ΩA

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

V1 = 6 VR1 = 5 ΩV2 = 24 VR2 = 3 ΩR3 = 2 Ω
VA = V
3.Medium
R1​5 Ω+−V1​6 VR2​20 Ω+−V2​10 VI2​R3​8 Ω−+V3​12 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 6 VR1 = 5 ΩV2 = 10 VR2 = 20 ΩV3 = 12 VR3 = 8 Ω
I2 = A
4.Medium
R1​ = 15 ΩR3​ = 2 Ω+−V1​10 VR2​3 ΩAR4​2 ΩBIs​2 A

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

V1 = 10 VIs = 2 AR1 = 15 ΩR2 = 3 ΩR3 = 2 ΩR4 = 2 Ω
VB = V
5.Hard
R1​ = 3 ΩR2​ = 15 ΩR4​ = 25 Ω+−V1​10 VR3​20 ΩAR5​12 ΩBIs​3 A−+V2​6 V

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

V1 = 10 VIs = 3 AV2 = 6 VR1 = 3 ΩR2 = 15 ΩR3 = 20 ΩR4 = 25 ΩR5 = 12 Ω
VA = V
6.Hard
R1​ = 4 ΩIR1​R2​ = 12 ΩR4​ = 25 Ω+−V1​9 VR3​4 ΩAR5​3 ΩBIs​4 A−+V2​5 V

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

V1 = 9 VIs = 4 AV2 = 5 VR1 = 4 ΩR2 = 12 ΩR3 = 4 ΩR4 = 25 ΩR5 = 3 Ω
IR1 = A

Answer key

  1. 1. R2 = 9.943 Ω
  2. 2. VA = 8.903 V
  3. 3. I2 = 0.4733 A
  4. 4. VB = −2.256 V
  5. 5. VA = 5.149 V
  6. 6. IR1 = 0.9548 A

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