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​18 VR2​6 ΩIR2​AIs​2 A

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

V1 = 18 VIs = 2 AR1 = 8 ΩR2 = 6 Ω
IR2 = A
2.Easy
R1​ = 6 Ω+−V1​24 VR2​2 ΩAIs​1 A

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

V1 = 24 VIs = 1 AR1 = 6 ΩR2 = 2 Ω
VA = V
3.Medium
R1​ = 10 ΩR3​ = 2 Ω+−V1​9 VR2​20 ΩAR4​12 ΩBIs​5 A

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

V1 = 9 VIs = 5 AR1 = 10 ΩR2 = 20 ΩR3 = 2 ΩR4 = 12 Ω
PIs = W
4.Medium
R1​ = 6 ΩR3​ = 2 Ω+−V1​10 VR2​6 ΩAR4​5 ΩBIs​4 A

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

V1 = 10 VIs = 4 AR1 = 6 ΩR2 = 6 ΩR3 = 2 ΩR4 = 5 Ω
VB = V
5.Hard
R1​ = 12 ΩIR1​R2​ = 15 ΩR4​ = 8 Ω+−V1​18 VR3​6 ΩAR5​2 ΩBIs​5 A+−V2​36 V

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

V1 = 18 VIs = 5 AV2 = 36 VR1 = 12 ΩR2 = 15 ΩR3 = 6 ΩR4 = 8 ΩR5 = 2 Ω
IR1 = A
6.Hard
R1​ = 5 ΩR3​ = 5 Ω+−V1​12 VR2​8 ΩAR4​8 ΩB0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 12 VR1 = 5 ΩR2 = 8 ΩR3 = 5 ΩR4 = 8 Ωg = 0.2 A/V
VA = V

Answer key

  1. 1. IR2 = 2.429 A
  2. 2. VA = 7.5 V
  3. 3. PIs = 143.2 W
  4. 4. VB = 12.5 V
  5. 5. IR1 = 0.8511 A
  6. 6. VA = 8.607 V

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