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​ = 2 Ω+−V1​12 VR2​?AIs​3 A

The node voltage at A is measured as VA = 7.5 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 3 AR1 = 2 ΩVA = 7.5 V
R2 = Ω
2.Easy
R1​ = 8 ΩR2​ = 12 ΩIR2​+−V1​18 VR3​4 ΩA+−V2​18 V

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

V1 = 18 VV2 = 18 VR1 = 8 ΩR2 = 12 ΩR3 = 4 Ω
IR2 = A
3.Medium
R1​ = 3 ΩR3​ = 2 Ω+−V1​10 VR2​4 ΩAR4​10 ΩBIs​5 A

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

V1 = 10 VIs = 5 AR1 = 3 ΩR2 = 4 ΩR3 = 2 ΩR4 = 10 Ω
VA = V
4.Medium
R1​ = 3 ΩR3​ = 3 Ω+−V1​30 VR2​8 ΩAR4​10 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 3 ΩR2 = 8 ΩR3 = 3 ΩR4 = 10 Ω
PIs = W
5.Hard
R1​ = 6 ΩR3​ = 8 Ω+−V1​30 VR2​25 ΩAR4​4 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 = 30 VR1 = 6 ΩR2 = 25 ΩR3 = 8 ΩR4 = 4 Ωg = 0.25 A/V
VA = V
6.Hard
R1​ = 2 ΩR3​ = 3 Ω+−V1​5 VR2​15 ΩAR4​3 ΩIR4​B0.5·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 current IR4 through R4 in the direction of the arrow.

V1 = 5 VR1 = 2 ΩR2 = 15 ΩR3 = 3 ΩR4 = 3 Ωg = 0.5 A/V
IR4 = A

Answer key

  1. 1. R2 = 1.429 Ω
  2. 2. IR2 = −0.8182 A
  3. 3. VA = 11.25 V
  4. 4. PIs = 157.2 W
  5. 5. VA = 24.19 V
  6. 6. IR4 = 2.155 A

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