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​ = 6 Ω+−V1​24 VR2​6 ΩIR2​AIs​2 A

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

V1 = 24 VIs = 2 AR1 = 6 ΩR2 = 6 Ω
IR2 = A
2.Easy
R1​ = 3 Ω+−V1​8 VR2​2 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 3 ΩR2 = 2 Ω
PIs = W
3.Medium
R1​ = 10 ΩR3​ = 10 Ω+−V1​30 VR2​12 ΩAR4​12 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 10 ΩR2 = 12 ΩR3 = 10 ΩR4 = 12 Ω
VA = V
4.Medium
R1​ = 4 ΩIR1​R3​ = 4 Ω+−V1​18 VR2​6 ΩAR4​6 ΩBIs​1 A

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

V1 = 18 VIs = 1 AR1 = 4 ΩR2 = 6 ΩR3 = 4 ΩR4 = 6 Ω
IR1 = A
5.Hard
R1​ = 15 ΩR2​ = 8 ΩR4​ = 2 Ω+−V1​12 VR3​12 ΩAR5​5 ΩBIs​1.5 A+−V2​6 V

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

V1 = 12 VIs = 1.5 AV2 = 6 VR1 = 15 ΩR2 = 8 ΩR3 = 12 ΩR4 = 2 ΩR5 = 5 Ω
VB = V
6.Hard
R1​ = 5 ΩR3​ = 12 Ω+−V1​30 VR2​6 ΩAR4​3 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 = 30 VR1 = 5 ΩR2 = 6 ΩR3 = 12 ΩR4 = 3 Ωg = 0.1 A/V
VA = V

Answer key

  1. 1. IR2 = 3 A
  2. 2. PIs = 11.2 W
  3. 3. VA = 22.65 V
  4. 4. IR1 = 2.032 A
  5. 5. VB = 6.331 V
  6. 6. VA = 14.52 V

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