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 Ω+−V1​6 VR2​8 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 5 ΩR2 = 8 Ω
PIs = W
2.Easy
R1​ = 6 ΩR2​ = 10 Ω+−V1​18 VR3​2 ΩIR3​A+−V2​20 V

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

V1 = 18 VV2 = 20 VR1 = 6 ΩR2 = 10 ΩR3 = 2 Ω
IR3 = A
3.Medium
−+Vs​ = 8 VIs​4 AAR1​2 ΩR2​6 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 = 4 AVs = 8 VR1 = 2 ΩR2 = 6 Ω
VA = V
4.Medium
R1​ = 8 ΩIR1​R3​ = 3 Ω+−V1​30 VR2​12 ΩAR4​3 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 8 ΩR2 = 12 ΩR3 = 3 ΩR4 = 3 Ω
IR1 = A
5.Hard
R1​ = 3 ΩR3​ = 25 Ω+−V1​12 VR2​5 ΩAR4​6 ΩB0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 12 VR1 = 3 ΩR2 = 5 ΩR3 = 25 ΩR4 = 6 Ωg = 0.5 A/V
VB = V
6.Hard
R1​ = 5 ΩR2​ = 4 ΩIR2​R4​ = 4 Ω+−V1​6 VR3​30 ΩAR5​6 ΩBIs​2 A−+V2​30 V

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

V1 = 6 VIs = 2 AV2 = 30 VR1 = 5 ΩR2 = 4 ΩR3 = 30 ΩR4 = 4 ΩR5 = 6 Ω
IR2 = A

Answer key

  1. 1. PIs = 6.769 W
  2. 2. IR3 = 3.261 A
  3. 3. VA = 4 V
  4. 4. IR1 = 1.833 A
  5. 5. VB = 22.29 V
  6. 6. IR2 = 1.717 A

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