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​2 Ω+−V1​20 VR2​4 Ω+−V2​8 VR3​4 Ω+−V3​20 VA

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

V1 = 20 VR1 = 2 ΩV2 = 8 VR2 = 4 ΩV3 = 20 VR3 = 4 Ω
VA = V
2.Easy
R1​ = 3 Ω+−V1​20 VR2​3 ΩIR2​AIs​2 A

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

V1 = 20 VIs = 2 AR1 = 3 ΩR2 = 3 Ω
IR2 = A
3.Medium
−+Vs​ = 10 VIs​1.5 AAR1​4 ΩR2​2 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 = 1.5 AVs = 10 VR1 = 4 ΩR2 = 2 Ω
VB = V
4.Medium
−+Vs​ = 12 VIx​Is​1 AAR1​5 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 current Ix through the voltage source, from A to B as shown by the arrow.

Is = 1 AVs = 12 VR1 = 5 ΩR2 = 15 Ω
Ix = A
5.Hard
R1​ = 25 ΩR3​ = 25 Ω+−V1​24 VR2​3 ΩAR4​25 ΩIR4​B0.25·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.25·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 24 VR1 = 25 ΩR2 = 3 ΩR3 = 25 ΩR4 = 25 Ωg = 0.25 A/V
IR4 = A
6.Hard
R1​ = 4 ΩR3​ = 8 Ω+−V1​18 VR2​2 ΩAR4​8 ΩIR4​B0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 18 VR1 = 4 ΩR2 = 2 ΩR3 = 8 ΩR4 = 8 Ωg = 0.2 A/V
IR4 = A

Answer key

  1. 1. VA = 17 V
  2. 2. IR2 = 4.333 A
  3. 3. VB = 5.333 V
  4. 4. Ix = 0.85 A
  5. 5. IR4 = 0.5188 A
  6. 6. IR4 = 1.026 A

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