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​5 Ω+−V1​12 VR2​10 Ω+−V2​12 VR3​2 Ω+−V3​24 VA

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

V1 = 12 VR1 = 5 ΩV2 = 12 VR2 = 10 ΩV3 = 24 VR3 = 2 Ω
VA = V
2.Easy
R1​ = 6 ΩR2​ = 5 Ω+−V1​10 VR3​8 ΩIR3​A+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 6 ΩR2 = 5 ΩR3 = 8 Ω
IR3 = A
3.Medium
R1​ = 6 ΩR3​ = 2 Ω+−V1​18 VR2​10 ΩAR4​12 ΩBIs​2.5 A

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

V1 = 18 VIs = 2.5 AR1 = 6 ΩR2 = 10 ΩR3 = 2 ΩR4 = 12 Ω
VA = V
4.Medium
−+Vs​ = 10 VIs​2.5 AAR1​3 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 = 2.5 AVs = 10 VR1 = 3 ΩR2 = 6 Ω
VB = V
5.Hard
R1​ = 3 ΩR2​ = 15 ΩR4​ = 3 Ω+−V1​18 VR3​30 ΩAR5​8 ΩBIs​4 A+−V2​6 V

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

V1 = 18 VIs = 4 AV2 = 6 VR1 = 3 ΩR2 = 15 ΩR3 = 30 ΩR4 = 3 ΩR5 = 8 Ω
VB = V
6.Hard
R1​ = 8 ΩR3​ = 10 Ω+−V1​5 VR2​8 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 3.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 8 ΩR2 = 8 ΩR3 = 10 ΩR4 = 20 ΩVA = 3.5 V
Is = A

Answer key

  1. 1. VA = 19.5 V
  2. 2. IR3 = 1.339 A
  3. 3. VA = 15.21 V
  4. 4. VB = 11.67 V
  5. 5. VB = 13.45 V
  6. 6. Is = 0.55 A

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