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​2 Ω+−V1​15 VR2​3 Ω+−V2​6 VR3​12 Ω+−V3​18 VA

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

V1 = 15 VR1 = 2 ΩV2 = 6 VR2 = 3 ΩV3 = 18 VR3 = 12 Ω
VA = V
2.Easy
R1​ = 8 ΩIR1​+−V1​8 VR2​5 ΩAIs​1 A

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

V1 = 8 VIs = 1 AR1 = 8 ΩR2 = 5 Ω
IR1 = A
3.Medium
R1​4 Ω+−V1​6 VR2​8 Ω+−V2​9 VI2​R3​3 Ω+−V3​15 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 = 4 ΩV2 = 9 VR2 = 8 ΩV3 = 15 VR3 = 3 Ω
I2 = A
4.Medium
R1​ = 20 ΩR3​ = 15 ΩIR3​+−V1​9 VR2​15 ΩAR4​4 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 20 ΩR2 = 15 ΩR3 = 15 ΩR4 = 4 Ω
IR3 = A
5.Hard
R1​ = 5 ΩR2​ = 12 ΩR4​ = 12 Ω+−V1​12 VR3​30 ΩAR5​2 ΩBIs​5 A+−V2​12 V

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

V1 = 12 VIs = 5 AV2 = 12 VR1 = 5 ΩR2 = 12 ΩR3 = 30 ΩR4 = 12 ΩR5 = 2 Ω
VB = V
6.Hard
R1​ = 8 ΩR3​ = 25 Ω+−V1​10 VR2​25 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 16 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 8 ΩR2 = 25 ΩR3 = 25 ΩR4 = 6 ΩVA = 16 V
Is = A

Answer key

  1. 1. VA = 12 V
  2. 2. IR1 = 0.2308 A
  3. 3. I2 = −0.2206 A
  4. 4. IR3 = 0.285 A
  5. 5. VB = −5.224 V
  6. 6. Is = 9.848 A

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