# Fundamental Physics/Electronics/Inductors

## Inductor

The foundation of modern electrical engineering was the discovery by Faraday that when the magnetic flux through a loop of wire was varied, a voltage was set up in the wire.

This process is called electromagnetic induction.

• A conductor wound in the form of a coil is called an inductor (or solenoid)
• An inductor has a strong magnetic field that has many uses
• Inductance opposes current change
• An inductor may have its inductance increased by:-
• introducing an iron core through the centre of the turns

### Inductor

Inductor is a electric component that can store magnetic field energy

### Construction

Capacitor is made from a straight line conductor of several circular turns

$L=N\mu {\frac {l}{A}}$ ## Inductor in DC Circuit

### Magnetic Intensity Strength

Measurement of magnetic strength

$B=LI$ ### Current

$I={\frac {B}{L}}$ ### Inductance

Inductance has a symbol L measured in Henry unit H

$L={\frac {B}{I}}$ For a staright line conductor

$L={\frac {\mu }{2\pi r}}$ For a circular loop

$L={\frac {\mu }{2r}}$ For a coil of N circular loops conductor

$L={\frac {N\mu }{l}}$ ## Inductor in AC Circuit

### Voltage

$v_{L}=L{\frac {di_{L}}{dt}}$ ### Current

$i_{L}={\frac {1}{L}}\int {dv_{L}}{dt}$ ### Reactance

Resistance to the AC current flow

$X_{C}={\frac {v_{L}}{i_{L}}}={\frac {L{\frac {di_{L}}{dt}}}{{\frac {1}{L}}\int {dv_{L}}{dt}}}$ In frequency domain

$X_{L}(j\omega )=j\omega L$ In phasor domain

$X_{L}(\omega \theta )=\omega L\angle 90$ ### Impedance

Resistance to the AC current flow

$Z_{L}=R_{L}+X_{L}$ In frequency domain

$Z_{L}=R_{L}+j\omega L$ $Z_{C}={\frac {1+j\omega T}{R_{L}}}$ In phasor domain

$Z_{L}=R_{L}\angle 0+j\omega L\angle 90$ $Z_{L}={\sqrt {R_{L}^{2}+(j\omega L)^{2}}}\angle \omega T$ ### Time Constant

$T={\frac {L}{R_{L}}}$ ### Power

Power of the capacitor

$p={\frac {1}{2}}Li^{2}$ ## Inductor Configuration

### Inductors in Series

For n inductor connected adjacent to each other as shown

The total resistance

$L_{t}=L_{1}+L_{2}+...+L_{n}$ For 2 series resistor of same value

$L_{t}=L_{1}+L_{2}=L+L=2L$ ### Inductors in parallel

For n inductors connected facing each other as shown

The total inductance

${\frac {1}{L_{1}}}+{\frac {1}{L_{2}}}+...+{\frac {1}{L_{n}}}$ For 2 parallel resistor of same value

${\frac {1}{L_{t}}}={\frac {1}{L_{1}}}+{\frac {1}{L_{2}}}={\frac {L_{1}+L_{2}}{L_{1}L_{2}}}={\frac {L+L}{LL}}={\frac {2L}{LL}}={\frac {2}{L}}$ $L_{t}={\frac {1}{2}}L$ 