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​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
2.Easy
R1​ = 8 ΩIR1​R2​ = 10 Ω+−V1​18 VR3​2 ΩA+−V2​20 V

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

V1 = 18 VV2 = 20 VR1 = 8 ΩR2 = 10 ΩR3 = 2 Ω
IR1 = A
3.Medium
R1​ = 6 ΩR3​ = 20 Ω+−V1​30 VR2​4 ΩAR4​12 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 6 ΩR2 = 4 ΩR3 = 20 ΩR4 = 12 Ω
PIs = W
4.Medium
R1​ = 3 ΩR3​ = 12 Ω+−V1​10 VR2​4 ΩAR4​10 ΩBIs​4 A

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

V1 = 10 VIs = 4 AR1 = 3 ΩR2 = 4 ΩR3 = 12 ΩR4 = 10 Ω
VB = V
5.Hard
R1​ = 4 ΩR3​ = 8 Ω+−V1​30 VR2​10 ΩAR4​2 ΩIR4​B0.25·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 current IR4 through R4 in the direction of the arrow.

V1 = 30 VR1 = 4 ΩR2 = 10 ΩR3 = 8 ΩR4 = 2 Ωg = 0.25 A/V
IR4 = A
6.Hard
R1​ = 8 ΩR3​ = 6 Ω+−V1​12 VR2​15 ΩAR4​25 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 = 12 VR1 = 8 ΩR2 = 15 ΩR3 = 6 ΩR4 = 25 Ωg = 0.05 A/V
VB = V

Answer key

  1. 1. VA = 7.5 V
  2. 2. IR1 = 1.517 A
  3. 3. PIs = 141.8 W
  4. 4. VB = 25.54 V
  5. 5. IR4 = 5.625 A
  6. 6. VB = 8.565 V

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