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.

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

Magnetic of Inductance

$B = I \cdot L$

Magnetic of Turns

Φ = N B

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

$\frac{d\phi}{dt} = \frac{dNB}{dt} = N \frac{dB}{dt} + B \frac{dN}{dt} = N \frac{dB}{dt}$

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 90^o (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/R_L

When there is a change of angle, the frequency also changes. This can be used to shift the frequency:

f = ( 2π / Tanθ ) ( R_L / L )

As frequency is one over time:

t = ( Tanθ / 2π ) (L / R_L )

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 R_L

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.

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