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​ = 4 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 = 4 ΩR2 = 4 Ω
IR2 = A
2.Easy
R1​3 Ω+−V1​20 VR2​2 Ω+−V2​12 VR3​8 ΩA

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

V1 = 20 VR1 = 3 ΩV2 = 12 VR2 = 2 ΩR3 = 8 Ω
VA = V
3.Medium
R1​ = 10 ΩR3​ = 20 ΩIR3​+−V1​24 VR2​20 ΩAR4​4 ΩBIs​2.5 A

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

V1 = 24 VIs = 2.5 AR1 = 10 ΩR2 = 20 ΩR3 = 20 ΩR4 = 4 Ω
IR3 = A
4.Medium
R1​ = 15 ΩR3​ = 8 Ω+−V1​9 VR2​12 ΩAR4​4 ΩBIs​1.5 A

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

V1 = 9 VIs = 1.5 AR1 = 15 ΩR2 = 12 ΩR3 = 8 ΩR4 = 4 Ω
VA = V
5.Hard
R1​ = 15 ΩR2​ = 15 ΩR4​ = 3 ΩIR4​+−V1​24 VR3​8 ΩAR5​5 ΩBIs​1 A+−V2​5 V

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

V1 = 24 VIs = 1 AV2 = 5 VR1 = 15 ΩR2 = 15 ΩR3 = 8 ΩR4 = 3 ΩR5 = 5 Ω
IR4 = A
6.Hard
R1​ = 2 ΩR2​ = 2 ΩR4​ = 2 Ω+−V1​12 VR3​10 ΩAR5​2 ΩBIs​2.5 A+−V2​10 V

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

V1 = 12 VIs = 2.5 AV2 = 10 VR1 = 2 ΩR2 = 2 ΩR3 = 10 ΩR4 = 2 ΩR5 = 2 Ω
VB = V

Answer key

  1. 1. IR2 = −0.5 A
  2. 2. VA = 13.22 V
  3. 3. IR3 = 0.1957 A
  4. 4. VA = 4.714 V
  5. 5. IR4 = 0.09471 A
  6. 6. VB = 4.107 V

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