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​ = 10 Ω+−V1​20 VR2​?AIs​2 A

The node voltage at A is measured as VA = 22.5 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 2 AR1 = 10 ΩVA = 22.5 V
R2 = Ω
2.Easy
R1​ = 3 ΩR2​ = 5 Ω+−V1​6 VR3​4 ΩIR3​A+−V2​8 V

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

V1 = 6 VV2 = 8 VR1 = 3 ΩR2 = 5 ΩR3 = 4 Ω
IR3 = A
3.Medium
R1​10 Ω+−V1​10 VR2​6 Ω+−V2​12 VR3​20 Ω+−V3​6 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 = 10 VR1 = 10 ΩV2 = 12 VR2 = 6 ΩV3 = 6 VR3 = 20 Ω
I3 = A
4.Medium
R1​ = 8 ΩR3​ = 15 Ω+−V1​6 VR2​3 ΩAR4​2 ΩBIs​5 A

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

V1 = 6 VIs = 5 AR1 = 8 ΩR2 = 3 ΩR3 = 15 ΩR4 = 2 Ω
VA = V
5.Hard
R1​ = 10 ΩR2​ = 8 ΩIR2​R4​ = 5 Ω+−V1​18 VR3​3 ΩAR5​20 ΩBIs​1 A−+V2​9 V

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

V1 = 18 VIs = 1 AV2 = 9 VR1 = 10 ΩR2 = 8 ΩR3 = 3 ΩR4 = 5 ΩR5 = 20 Ω
IR2 = A
6.Hard
R1​ = 30 ΩIR1​R2​ = 10 ΩR4​ = 6 Ω+−V1​6 VR3​15 ΩAR5​6 ΩBIs​6 A−+V2​30 V

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

V1 = 6 VIs = 6 AV2 = 30 VR1 = 30 ΩR2 = 10 ΩR3 = 15 ΩR4 = 6 ΩR5 = 6 Ω
IR1 = A

Answer key

  1. 1. R2 = 12.86 Ω
  2. 2. IR3 = 1.149 A
  3. 3. I3 = −0.2211 A
  4. 4. VA = 2.588 V
  5. 5. IR2 = 0.514 A
  6. 6. IR1 = 0.6406 A

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