# 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.

**Inductance of Inductor:**

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

**Voltage across 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.
- i
_{to}= 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 _{L }= ωL = 2πfL**

Where

- X
_{L }is 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 = X _{L}/ESR**

Where

- X
_{L }is 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/X _{L}**

Where

- DF is the dissipation factor
- δ is the angle between capacitive reactance victor & negative axis.
- X
_{C }is 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 Li ^{2}**

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:

**P**_{av}** = Li ^{2} / 2t**

Where

**t**= 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:

**During Discharging:**

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

Where

- I
_{C}is the current of the inductor - I
_{0}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”**

Where:

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

**Spiral Coil Inductance Formula**

Where:

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

**Spiral Coil Wire Length Formula**

**Conical Coil Inductance Formula**

Where:

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

Related Formulas and Equations Posts:

- Resistance, Capacitance & Inductance in Series-Parallel – Equation & Formulas
- Basic Electrical Engineering Formulas and Equations
- Basic Electrical Quantities Formulas
- Power Formulas in DC and AC Single-Phase & Three-Phase Circuits
- Losses in Electrical Machines – Formulas and Equations
- DC Generator Formulas and Equations
- Power, Voltage and EMF Equation of a DC Motor – Formulas
- Synchronous Generator and Alternator Formulas & Equations
- Synchronous, Stepper and AC Motors Formulas and Equations
- Induction Motor & Linear Induction Motors Formulas & Equations
- Transformer Formulas and Equations
- Electrical & Electronics Engineering Formulas & Equations
- Electrical & Electronics Elements & Symbols