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​8 VR2​3 ΩAIs​1 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 8 VIs = 1 AR1 = 2 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​ = 4 Ω+−V1​6 VR2​8 ΩIR2​AIs​2 A

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

V1 = 6 VIs = 2 AR1 = 4 ΩR2 = 8 Ω
IR2 = A
3.Medium
R1​ = 5 ΩR3​ = 6 Ω+−V1​30 VR2​15 ΩAR4​2 ΩBIs​1.5 A

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

V1 = 30 VIs = 1.5 AR1 = 5 ΩR2 = 15 ΩR3 = 6 ΩR4 = 2 Ω
VA = V
4.Medium
−+Vs​ = 10 VIx​Is​1.5 AAR1​8 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 = 1.5 AVs = 10 VR1 = 8 ΩR2 = 15 Ω
Ix = A
5.Hard
R1​ = 5 ΩR3​ = 25 Ω+−V1​9 VR2​3 ΩAR4​10 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 = 9 VR1 = 5 ΩR2 = 3 ΩR3 = 25 ΩR4 = 10 Ωg = 0.1 A/V
VA = V
6.Hard
R1​ = 15 ΩR3​ = 4 Ω+−V1​24 VR2​3 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 10 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 15 ΩR2 = 3 ΩR3 = 4 ΩR4 = 30 ΩVA = 10 V
Is = A

Answer key

  1. 1. PIs = 6 W
  2. 2. IR2 = −0.1667 A
  3. 3. VA = 16.28 V
  4. 4. Ix = 0.9565 A
  5. 5. VA = 3.375 V
  6. 6. Is = 3.053 A

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