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​ = 8 ΩR2​ = 6 Ω+−V1​24 VR3​5 ΩIR3​A+−V2​24 V

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

V1 = 24 VV2 = 24 VR1 = 8 ΩR2 = 6 ΩR3 = 5 Ω
IR3 = A
2.Easy
R1​ = 3 Ω+−V1​6 VR2​4 ΩIR2​AIs​3 A

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

V1 = 6 VIs = 3 AR1 = 3 ΩR2 = 4 Ω
IR2 = A
3.Medium
R1​4 Ω+−V1​18 VR2​5 Ω+−V2​18 VI2​R3​12 ΩA

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 = 18 VR1 = 4 ΩV2 = 18 VR2 = 5 ΩR3 = 12 Ω
I2 = A
4.Medium
−+Vs​ = 8 VIs​4 AAR1​20 ΩR2​6 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VB (measured from ground).

Is = 4 AVs = 8 VR1 = 20 ΩR2 = 6 Ω
VB = V
5.Hard
R1​ = 15 ΩR3​ = 5 Ω+−V1​30 VR2​10 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 18 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 30 VR1 = 15 ΩR2 = 10 ΩR3 = 5 ΩR4 = 10 ΩVA = 18 V
Is = A
6.Hard
R1​ = 4 ΩIR1​R2​ = 6 ΩR4​ = 12 Ω+−V1​10 VR3​3 ΩAR5​2 ΩBIs​5 A−+V2​30 V

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

V1 = 10 VIs = 5 AV2 = 30 VR1 = 4 ΩR2 = 6 ΩR3 = 3 ΩR4 = 12 ΩR5 = 2 Ω
IR1 = A

Answer key

  1. 1. IR3 = 2.847 A
  2. 2. IR2 = 2.143 A
  3. 3. I2 = 0.5625 A
  4. 4. VB = 20.31 V
  5. 5. Is = 3.3 A
  6. 6. IR1 = 2.208 A

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