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 ΩIR1​R2​ = 12 Ω+−V1​20 VR3​8 ΩA+−V2​6 V

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

V1 = 20 VV2 = 6 VR1 = 3 ΩR2 = 12 ΩR3 = 8 Ω
IR1 = A
2.Easy
R1​ = 4 Ω+−V1​24 VR2​12 ΩIR2​AIs​1 A

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

V1 = 24 VIs = 1 AR1 = 4 ΩR2 = 12 Ω
IR2 = A
3.Medium
R1​ = 10 ΩR3​ = 8 Ω+−V1​12 VR2​8 ΩAR4​2 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 10 ΩR2 = 8 ΩR3 = 8 ΩR4 = 2 Ω
VA = V
4.Medium
−+Vs​ = 8 VIs​1 AAR1​10 ΩR2​10 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 = 1 AVs = 8 VR1 = 10 ΩR2 = 10 Ω
VB = V
5.Hard
R1​ = 2 Ω−+Vs​ = 12 VIx​+−V1​12 VR2​8 ΩAR3​20 ΩBIs​4 A

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 current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 12 VIs = 4 AVs = 12 VR1 = 2 ΩR2 = 8 ΩR3 = 20 Ω
Ix = A
6.Hard
R1​ = 25 ΩR3​ = 3 Ω+−V1​10 VR2​8 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 4 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 25 ΩR2 = 8 ΩR3 = 3 ΩR4 = 6 ΩVA = 4 V
Is = A

Answer key

  1. 1. IR1 = 2.256 A
  2. 2. IR2 = 1.25 A
  3. 3. VA = 4.308 V
  4. 4. VB = 9 V
  5. 5. Ix = −2.704 A
  6. 6. Is = 1.057 A

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