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

Inductor and DC electricity
Electric charge
 * $$B = L I$$ . 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
 * $$Z=\frac{v(t)}{i(t)}=R_L + X_L=R + \omega L \angle 90=R + j \omega L=R + sL$$

Reactance
 * $$X_L = \omega L \angle 90= j \omega L= sL$$

Phase angle
 * $$Tan \theta=\omega T$$

Time constant
 * $$T=\frac{L}{R}$$