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​6 VR2​10 Ω+−V2​18 VR3​2 Ω+−V3​10 VA

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

V1 = 6 VR1 = 4 ΩV2 = 18 VR2 = 10 ΩV3 = 10 VR3 = 2 Ω
VA = V
2.Easy
R1​ = 6 ΩIR1​+−V1​18 VR2​5 ΩAIs​2 A

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

V1 = 18 VIs = 2 AR1 = 6 ΩR2 = 5 Ω
IR1 = A
3.Medium
R1​ = 10 ΩR3​ = 4 Ω+−V1​24 VR2​2 ΩAR4​2 ΩBIs​1.5 A

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

V1 = 24 VIs = 1.5 AR1 = 10 ΩR2 = 2 ΩR3 = 4 ΩR4 = 2 Ω
VA = V
4.Medium
R1​ = 8 ΩR3​ = 4 Ω+−V1​6 VR2​8 ΩAR4​8 ΩBIs​3 A

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

V1 = 6 VIs = 3 AR1 = 8 ΩR2 = 8 ΩR3 = 4 ΩR4 = 8 Ω
VB = V
5.Hard
R1​ = 25 Ω−+Vs​ = 12 V+−V1​36 VR2​4 ΩAR3​10 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 node voltage VB (measured from ground).

V1 = 36 VIs = 4 AVs = 12 VR1 = 25 ΩR2 = 4 ΩR3 = 10 Ω
VB = V
6.Hard
R1​ = 25 ΩR3​ = 3 Ω+−V1​5 VR2​4 ΩAR4​6 ΩB0.1·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.1·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 5 VR1 = 25 ΩR2 = 4 ΩR3 = 3 ΩR4 = 6 Ωg = 0.1 A/V
VA = V

Answer key

  1. 1. VA = 9.765 V
  2. 2. IR1 = 0.7273 A
  3. 3. VA = 3.783 V
  4. 4. VB = 13.5 V
  5. 5. VB = 22.87 V
  6. 6. VA = 0.598 V

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