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Formula and Equations For Inductor and Inductance

Inductor and Inductance Formulas and Equations

The following formulas and equations can be used to calculate the inductance and related quantities of different shapes of inductors as follow.

Formula and Equations For Inductor and Inductance

Inductance of Inductor:

The inductance of the inductor from the basic formula of inductor:

inductance

Voltage across Inductor:

Voltage Across Inductor

Current of the Inductor:

Current Of The Inductor

Where

  • V is the voltage across inductor
  • L is the inductance of the inductor in Henry
  • Di/dt is the instantaneous rate of current change through the inductor.
  • ito = current at time t = 0.

Reactance of the Inductor:

Inductive reactance is the opposition of inductor to alternating current AC, which depends on its frequency f and is measured in Ohm just like resistance. Inductive reactance is calculated using:

X= ωL = 2πfL

Where

  • Xis the Inductive reactance
  • f is the applied frequency
  • L is the Inductance in Henry

Quality Factor of Inductor:

The efficiency of the inductor is known as quality factor & its measured by:

QF = XL/ESR

Where

  • Xis the Inductive reactance
  • ESR is the equivalent series resistance of the circuit.

Dissipation Factor of Inductor:

It is the inverse of the quality factor and it shows the power dissipation inside the inductor & its given by:

DF = tan δ = ESR/XL

Where

  • DF is the dissipation factor
  • δ is the angle between capacitive reactance victor & negative axis.
  • Xis the capacitive reactance
  • ESR is the equivalent series resistance of the circuit.

Energy Stored in an Inductor:

The energy E stored in inductor is given by:

E = ½ Li2

Where

  • E is the energy in joules
  • L is the inductance in Henry
  • i is the current in Amps

Related Posts:

Average Power of Inductor

The average power for the inductor is given by:

Pav = Li2 / 2t

Where

  • = is the time in seconds.

Inductor Current During Charge / Discharge:

Just like capacitor, the inductor takes up to 5 time constant to fully charge or discharge, during this time the current can be calculated by:

During Charging:

Instantaneous current of the inductor during charging is given by:

Inductor Charging

During Discharging:

The current during the discharging at any time t is given by:

Inductor discharging

Where

  • IC is the current of the inductor
  • I0 is the current at time t=0
  • t  is the time passed after supplying current.
  • τ = L/R is the time constant of the RL circuit

Related Posts:

Inductance Formulas

Helical Coil Inductance “Wheeler’s Formula”

Helical Coil Inductance - Wheeler’s Formula

Where:

  • L is the inductance
  • R is the radius
  • n is the number of turns
  • h is the height

Spiral Coil Inductance Formula

Spiral Coil Inductance Formula

Where:

  • OR is the outermost radius in inches
  • IR is the innermost radius in inches

Spiral Coil Wire Length Formula

Spiral Coil Wire Length Formula

Conical Coil Inductance Formula

Conical Coil Inductance Formula

Where:

  • θ is the angle outside the cone, (assume θ ≈ 15°)

Related Formulas and Equations Posts:

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