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​ = 3 ΩR2​ = 2 ΩIR2​+−V1​24 VR3​6 ΩA+−V2​8 V

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

V1 = 24 VV2 = 8 VR1 = 3 ΩR2 = 2 ΩR3 = 6 Ω
IR2 = A
2.Easy
R1​ = 12 Ω+−V1​10 VR2​?AIs​2 A

The node voltage at A is measured as VA = 5 V. Use nodal analysis to find the resistance R2.

V1 = 10 VIs = 2 AR1 = 12 ΩVA = 5 V
R2 = Ω
3.Medium
R1​ = 10 ΩR3​ = 6 Ω+−V1​6 VR2​12 ΩAR4​5 ΩBIs​1 A

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

V1 = 6 VIs = 1 AR1 = 10 ΩR2 = 12 ΩR3 = 6 ΩR4 = 5 Ω
VB = V
4.Medium
R1​ = 20 ΩR3​ = 15 Ω+−V1​9 VR2​3 ΩAR4​4 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 20 ΩR2 = 3 ΩR3 = 15 ΩR4 = 4 Ω
VA = V
5.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​12 VR2​6 ΩAR4​3 ΩB0.5·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 node voltage VB (measured from ground).

V1 = 12 VR1 = 4 ΩR2 = 6 ΩR3 = 6 ΩR4 = 3 Ωg = 0.5 A/V
VB = V
6.Hard
R1​ = 12 ΩR3​ = 2 Ω+−V1​9 VR2​2 ΩAR4​6 ΩIR4​B0.4·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.4·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 = 9 VR1 = 12 ΩR2 = 2 ΩR3 = 2 ΩR4 = 6 Ωg = 0.4 A/V
IR4 = A

Answer key

  1. 1. IR2 = 2 A
  2. 2. R2 = 2.069 Ω
  3. 3. VB = 4.475 V
  4. 4. VA = 1.515 V
  5. 5. VB = 11.08 V
  6. 6. IR4 = 0.4133 A

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