Inductors

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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

Contents

[edit] Inductance

L = N \frac {l}{A}

[edit] Magnetic of Inductance

B = I \cdot L

[edit] Magnetic of Turns

Φ = N B

[edit] Voltage of Coil's Inductance

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

[edit] Voltage of Coil's Turns

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

[edit] Reactance

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

[edit] Impedance

ZC = RC + XL = RL + jωL

[edit] 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 = ωLR = 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 )

[edit] Frequency Response

ω = 0,XL = 0, Shorted Circuit. I = 0
ω = 00,XL = 00, Opened Circuit. I ‡ 0
ω = 0,XL = RL, 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.

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