Electronics Bible/Inductor

Inductor is an electronics device made from a coil of many circular loops that can store energy as Magnetic field

Inductance

Inductance represents inductor's capability to store energy as Magnetic field . Inductor has a symbol $L$ and measured in unit Henry $H$

$L=\frac{B}{i}$

Inductor can be made from a coil of many circular loops that has inductance

$L=\mu i\frac{Nl}{A}$

From above

$L=\frac{B}{i}=\mu i\frac{Nl}{A}$

$\mu =\frac{B}{i^2}\frac{A}{Nl}$

Electricity response of inductor

Inductor and DC electricity

Electric charge

$B=LI$ . Ampere's law

Capacitance

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

Voltage

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

Inductor and AC electricity

Voltage

$v(t)=L\frac{d}{dt}i(t)$

Current

$i(t)=\frac{1}{L}\int v(t)dt$

Power

$p(t)=\frac{1}{2}L{i}^2(t)$

Impedance

$Z=\frac{v(t)}{i(t)}=R_L+X_L=R+\omega L\mathrm{\angle }90=R+j\omega L=R+sL$

Reactance

$X_L=\omega L\mathrm{\angle }90=j\omega L=sL$

Phase angle

$Tan\theta =\omega T$

Time constant

$T=\frac{L}{R}$