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 ΩR2​ = 2 Ω+−V1​6 VR3​8 ΩA+−V2​10 V

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

V1 = 6 VV2 = 10 VR1 = 3 ΩR2 = 2 ΩR3 = 8 Ω
VA = V
2.Easy
R1​ = 8 Ω+−V1​6 VR2​12 ΩAIs​2 A

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

V1 = 6 VIs = 2 AR1 = 8 ΩR2 = 12 Ω
PIs = W
3.Medium
R1​ = 8 ΩR3​ = 5 Ω+−V1​24 VR2​8 ΩAR4​20 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 8 ΩR2 = 8 ΩR3 = 5 ΩR4 = 20 Ω
VB = V
4.Medium
R1​ = 12 ΩR3​ = 5 ΩIR3​+−V1​24 VR2​3 ΩAR4​5 ΩBIs​1 A

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

V1 = 24 VIs = 1 AR1 = 12 ΩR2 = 3 ΩR3 = 5 ΩR4 = 5 Ω
IR3 = A
5.Hard
R1​ = 5 ΩR3​ = 25 Ω+−V1​18 VR2​6 ΩAR4​2 ΩB0.05·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 node voltage VB (measured from ground).

V1 = 18 VR1 = 5 ΩR2 = 6 ΩR3 = 25 ΩR4 = 2 Ωg = 0.05 A/V
VB = V
6.Hard
R1​ = 15 ΩIR1​−+Vs​ = 9 V+−V1​5 VR2​20 ΩAR3​20 ΩBIs​1.5 A

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 IR1 through R1 in the direction of the arrow.

V1 = 5 VIs = 1.5 AVs = 9 VR1 = 15 ΩR2 = 20 ΩR3 = 20 Ω
IR1 = A

Answer key

  1. 1. VA = 7.304 V
  2. 2. PIs = 26.4 W
  3. 3. VB = 33.1 V
  4. 4. IR3 = 0.7903 A
  5. 5. VB = 1.5 V
  6. 6. IR1 = −0.22 A

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