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.

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

Magnetic of Inductance

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

Magnetic of Turns

Φ = N B

Voltage of Coil's Inductance

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

Voltage of Coil's Turns

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

Reactance

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

Impedance

${\displaystyle Z_{C}=R_{C}+X_{L}=R_{L}+j\omega L}$

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 = ${\displaystyle {\omega L}{R}}$ = 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

${\displaystyle \omega =0,X_{L}=0}$, Shorted Circuit. I = 0

${\displaystyle \omega =00,X_{L}=00}$, Opened Circuit. I ‡ 0

${\displaystyle \omega =0,X_{L}=R_{L}}$, 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.