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 ΩR2​ = 2 Ω+−V1​8 VR3​4 ΩIR3​A+−V2​18 V

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

V1 = 8 VV2 = 18 VR1 = 5 ΩR2 = 2 ΩR3 = 4 Ω
IR3 = A
2.Easy
R1​ = 5 Ω+−V1​12 VR2​?AIs​2 A

The node voltage at A is measured as VA = 20 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 2 AR1 = 5 ΩVA = 20 V
R2 = Ω
3.Medium
R1​15 Ω+−V1​6 VR2​12 Ω+−V2​6 VI2​R3​12 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 = 15 ΩV2 = 6 VR2 = 12 ΩV3 = 15 VR3 = 12 Ω
I2 = A
4.Medium
−+Vs​ = 5 VIs​2 AAR1​2 ΩR2​15 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 AVs = 5 VR1 = 2 ΩR2 = 15 Ω
VB = V
5.Hard
R1​ = 3 ΩR3​ = 8 Ω+−V1​24 VR2​3 ΩAR4​25 ΩB0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 24 VR1 = 3 ΩR2 = 3 ΩR3 = 8 ΩR4 = 25 Ωg = 0.05 A/V
VA = V
6.Hard
R1​ = 2 ΩIR1​−+Vs​ = 3 V+−V1​10 VR2​2 ΩAR3​4 ΩBIs​0.5 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 IR1 through R1 in the direction of the arrow.

V1 = 10 VIs = 0.5 AVs = 3 VR1 = 2 ΩR2 = 2 ΩR3 = 4 Ω
IR1 = A

Answer key

  1. 1. IR3 = 2.789 A
  2. 2. R2 = 50 Ω
  3. 3. I2 = −0.2679 A
  4. 4. VB = 7.941 V
  5. 5. VA = 12.14 V
  6. 6. IR1 = 3.1 A

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