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 ΩR2​ = 12 Ω+−V1​15 VR3​5 ΩA+−V2​24 V

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

V1 = 15 VV2 = 24 VR1 = 6 ΩR2 = 12 ΩR3 = 5 Ω
VA = V
2.Easy
R1​ = 2 Ω+−V1​12 VR2​2 ΩIR2​AIs​1 A

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

V1 = 12 VIs = 1 AR1 = 2 ΩR2 = 2 Ω
IR2 = A
3.Medium
R1​ = 8 ΩIR1​R3​ = 2 Ω+−V1​10 VR2​10 ΩAR4​20 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 8 ΩR2 = 10 ΩR3 = 2 ΩR4 = 20 Ω
IR1 = A
4.Medium
R1​ = 10 ΩR3​ = 15 Ω+−V1​18 VR2​8 ΩAR4​10 ΩBIs​5 A

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

V1 = 18 VIs = 5 AR1 = 10 ΩR2 = 8 ΩR3 = 15 ΩR4 = 10 Ω
PIs = W
5.Hard
R1​ = 8 ΩR2​ = 15 ΩR4​ = 25 ΩIR4​+−V1​6 VR3​30 ΩAR5​25 ΩBIs​4 A+−V2​10 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 6 VIs = 4 AV2 = 10 VR1 = 8 ΩR2 = 15 ΩR3 = 30 ΩR4 = 25 ΩR5 = 25 Ω
IR4 = A
6.Hard
R1​ = 30 ΩR3​ = 20 Ω+−V1​5 VR2​15 ΩAR4​6 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 VA (measured from ground).

V1 = 5 VR1 = 30 ΩR2 = 15 ΩR3 = 20 ΩR4 = 6 Ωg = 0.25 A/V
VA = V

Answer key

  1. 1. VA = 10 V
  2. 2. IR2 = 3.5 A
  3. 3. IR1 = 1.303 A
  4. 4. PIs = 178.7 W
  5. 5. IR4 = 1.057 A
  6. 6. VA = 2.063 V

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