Electronics/Inductors

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:-
 * adding more turns
 * introducing an iron core through the centre of the turns

Inductance
Inductance is the property by which it opposes the change in current through a circuit.
 * $$L = N \frac {l}{A}$$

L = Inductance in Henry N = Number of turns in wire coil A = Area of coil in square ² meter l = Average length of coil in meters

Magnetic of Inductance

 * $$B = I \cdot L$$

L = Inductor in Henrys

Magnetic of Turns

 * Φ = N B A

A-area of cross section of the coil

Voltage of Coil's Inductance

 * $$\frac{dB}{dt} = \frac{dIL}{dt} = L \frac{dI}{dt} + I \frac{dL}{dt} = L \frac{dI}{dt}$$ = -ξ

Voltage of Coil's Turns

 * $$\frac{d\phi}{dt} = \frac{dNBA}{dt} = A (N \frac{dB}{dt} + B \frac{dN}{dt}) = A N \frac{dB}{dt}$$

Reactance

 * $$\frac{V}{I} = \frac {L \frac{dI}{dt}}{I} = j \omega L$$

Impedance

 * $$Z_C = R_C + X_L = R_L + j \omega L$$

Phase Angle
For an inductor without resistance, the voltage and current is out of phase by 90o (π/2 radians).

For an inductor with resistance, the voltage and current is out of phase by θ:
 * Tan θ = $${\omega L}{R}$$ = 2πf L/RL

When there is a change of angle, the frequency also changes. This can be used to shift the frequency:
 * f = ( 2π / Tanθ ) ( RL / L )

As frequency is one over time:
 * t = ( Tanθ / 2π ) (L / RL )

Frequency Response

 * $$\omega = 0, X_L = 0$$, Shorted Circuit. I = 0
 * $$\omega = 00, X_L = 00$$, Opened Circuit. I ‡ 0
 * $$\omega = 0, X_L = R_L$$, Shorted Circuit. I = V / 2 RL

I - can be drawn, at certain frequency the value of current does not change with. So this circuit can be used as a high pass filter.