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 Ω+−V1​6 VR2​?AIs​1 A

The node voltage at A is measured as VA = 6.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 1 AR1 = 3 ΩVA = 6.5 V
R2 = Ω
2.Easy
R1​ = 2 Ω+−V1​8 VR2​3 ΩAIs​1 A

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

V1 = 8 VIs = 1 AR1 = 2 ΩR2 = 3 Ω
VA = V
3.Medium
−+Vs​ = 6 VIx​Is​1 AAR1​15 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 = 6 VR1 = 15 ΩR2 = 15 Ω
Ix = A
4.Medium
−+Vs​ = 6 VIs​2.5 AAR1​12 ΩR2​4 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 VA (measured from ground).

Is = 2.5 AVs = 6 VR1 = 12 ΩR2 = 4 Ω
VA = V
5.Hard
R1​ = 15 ΩR3​ = 20 Ω+−V1​5 VR2​25 ΩAR4​3 ΩIR4​B0.05·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 current IR4 through R4 in the direction of the arrow.

V1 = 5 VR1 = 15 ΩR2 = 25 ΩR3 = 20 ΩR4 = 3 Ωg = 0.05 A/V
IR4 = A
6.Hard
R1​ = 3 ΩR3​ = 20 Ω+−V1​6 VR2​5 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 6 VR1 = 3 ΩR2 = 5 ΩR3 = 20 ΩR4 = 20 ΩVA = 9 V
Is = A

Answer key

  1. 1. R2 = 7.8 Ω
  2. 2. VA = 6 V
  3. 3. Ix = 0.7 A
  4. 4. VA = 3 V
  5. 5. IR4 = 0.2018 A
  6. 6. Is = 6.05 A

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