# Fundamental Physics/Electricity/Inductor

## 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

${\displaystyle L=N\mu {\frac {l}{A}}}$

## Inductor in DC Circuit

### Inductance

Inductance has a symbol L measured in Henry unit H

${\displaystyle L={\frac {B}{I}}}$

### Magnetic Intensity Strength

Measurement of magnetic strength

${\displaystyle B=LI}$

### Current

${\displaystyle I={\frac {B}{L}}}$

## Resistor in AC Circuit

### Voltage

${\displaystyle v_{L}=L{\frac {di_{L}}{dt}}}$

### Current

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

### Reactance

Resistance to the AC current flow

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

In frequency domain

${\displaystyle X_{L}(j\omega )=j\omega L}$

In phasor domain

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

### Impedance

Resistance to the AC current flow

${\displaystyle Z_{L}=R_{L}+X_{L}}$

In frequency domain

${\displaystyle Z_{L}=R_{L}+j\omega L}$
${\displaystyle Z_{C}={\frac {1+j\omega T}{R_{L}}}}$

In phasor domain

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

### Time Constant

${\displaystyle T={\frac {L}{R_{L}}}}$

### Power

Power of the capacitor

${\displaystyle p={\frac {1}{2}}Li^{2}}$