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​ = 3 Ω+−V1​24 VR2​3 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 3 ΩR2 = 3 Ω
VA = V
2.Easy
R1​12 Ω+−V1​6 VR2​4 Ω+−V2​15 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 = 12 ΩV2 = 15 VR2 = 4 ΩR3 = 2 Ω
VA = V
3.Medium
R1​ = 6 ΩIR1​R3​ = 4 Ω+−V1​9 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 = 9 VIs = 2.5 AR1 = 6 ΩR2 = 20 ΩR3 = 4 ΩR4 = 5 Ω
IR1 = A
4.Medium
R1​ = 12 ΩR3​ = 4 Ω+−V1​18 VR2​8 ΩAR4​12 ΩBIs​1.5 A

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

V1 = 18 VIs = 1.5 AR1 = 12 ΩR2 = 8 ΩR3 = 4 ΩR4 = 12 Ω
VB = V
5.Hard
R1​ = 5 ΩR2​ = 12 ΩIR2​R4​ = 6 Ω+−V1​9 VR3​12 ΩAR5​2 ΩBIs​4 A+−V2​6 V

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

V1 = 9 VIs = 4 AV2 = 6 VR1 = 5 ΩR2 = 12 ΩR3 = 12 ΩR4 = 6 ΩR5 = 2 Ω
IR2 = A
6.Hard
R1​ = 3 ΩR3​ = 8 Ω+−V1​18 VR2​20 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 17.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 18 VR1 = 3 ΩR2 = 20 ΩR3 = 8 ΩR4 = 30 ΩVA = 17.5 V
Is = A

Answer key

  1. 1. VA = 9 V
  2. 2. VA = 5.1 V
  3. 3. IR1 = 1.444 A
  4. 4. VB = 11.77 V
  5. 5. IR2 = −0.06736 A
  6. 6. Is = 1.481 A

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