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​ = 8 Ω+−V1​6 VR2​8 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 8 ΩR2 = 8 Ω
PIs = W
2.Easy
R1​ = 10 ΩIR1​+−V1​24 VR2​4 ΩAIs​3 A

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

V1 = 24 VIs = 3 AR1 = 10 ΩR2 = 4 Ω
IR1 = A
3.Medium
R1​ = 15 ΩR3​ = 12 Ω+−V1​9 VR2​3 ΩAR4​3 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 15 ΩR2 = 3 ΩR3 = 12 ΩR4 = 3 Ω
VB = V
4.Medium
−+Vs​ = 6 VIx​Is​1.5 AAR1​8 ΩR2​3 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 = 6 VR1 = 8 ΩR2 = 3 Ω
Ix = A
5.Hard
R1​ = 15 ΩR3​ = 8 Ω+−V1​15 VR2​6 ΩAR4​4 ΩB0.25·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 node voltage VB (measured from ground).

V1 = 15 VR1 = 15 ΩR2 = 6 ΩR3 = 8 ΩR4 = 4 Ωg = 0.25 A/V
VB = V
6.Hard
R1​ = 3 ΩR2​ = 8 ΩR4​ = 2 Ω+−V1​10 VR3​30 ΩAR5​8 ΩBIs​1 A−+V2​10 V

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

V1 = 10 VIs = 1 AV2 = 10 VR1 = 3 ΩR2 = 8 ΩR3 = 30 ΩR4 = 2 ΩR5 = 8 Ω
VA = V

Answer key

  1. 1. PIs = 45 W
  2. 2. IR1 = 0.8571 A
  3. 3. VB = 2.743 V
  4. 4. Ix = 1.636 A
  5. 5. VB = 4.286 V
  6. 6. VA = 5.664 V

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