Practical Electronics/Inductors

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Contents

[edit] Intro

Inductor is a device made from a straight wire conductor with several turns . This device when conducts current will generates Magnetic Field that has the same characteristic as Magnet's magnetic field another word, a tool used to store electric energy in the form of Magnetic Field


Inductance is defined as the capability to store electric energy in the form of Magnetic Field for a given current which is directly proportional to Permability, length of inductor, number of turns and inversely proportional to cross sectional area.

L = \frac{B}{I} = μN\frac{l}{A}

Inductor has a symbol . Inductance has a symbol L and measured in Henry which has the symbol H

[edit] Characteristics

[edit] Magnetic Field

When a voltage is applied across the inductor, current generates Electric Field . Change of Electric Field in the turns generates Magnetic Field perpendicular to Electric Field

B = I L

[edit] Inductance

Inductance is the ability to generartes Magnetic Field B for a given Current

L = \frac{B}{I}

[edit] Voltage

V_L = L \frac{dI}{dt} = \frac{dB}{dt}

[edit] Current

I_L = \frac{1}{L} \int V dt

[edit] Reactance

Reactance is defined as the ratio of Voltage over current

X_L = \frac {L \frac{dI}{dt}}{I}
XL = ωL/_90
XL = jωL
XL = sL

[edit] Impedance

Impedance is defined as the sum of Reactance and Resistance of Inductor . Since all conductor has Resistance

ZL = RL + XL
Z_L = \sqrt{R_L^2 + (\omega L)^2}/_Tan-1 \omega \frac{L}{R}
ZL = RL + jωL
ZL = RL + sL

[edit] Frequency Respond

Inductor is a device depends on frequency ω

  • ω = 0,XL = 0, Inductor Closed circuit, I ≠ 0
  • ω = 00,XL = 00, Capacitor Opened circuit, I = 0
  • \omega = \frac{R_L}{L}
XL = RL ,
Z_L = [(RL]⅓</math> ,
V_L = \frac {V}{2}
I_L = \frac {V}{2R_L}

With the value of I at three frequency points ω = 0, 00 , 1 / CRC I - f curve can be drawn to give a picture of current in the inductor over time

[edit] Phase Angle

When a Voltage is applied across inductor , current generates magnetic field . Change in curent generate change in magnetic field which generate voltage across inductor . Therefore, current will lead voltage

For ideal losses inductor which has no internal resistance, Current will lead Voltage an angle 90 . For Non - Ideal inductor which has an internal resistance, Current will lead Voltage an angle θ

Tanθ = ωLRL = 2π f \frac{L}{R_L}

Phase angle relates to time frequecy or time and the value of R and L . When there is a change in phase angle Time and frequency also change

f = (Tanθ/2π) \frac{R_L}{L}
t = (2π/Tanθ) \frac{L}{R_L}

If choosing L = 1 and R = 10n then the formulas above become

f = (Tanθ/2π) x 10n ≈ 0.3 x 10n Tanθ
t = (2π/Tanθ) x 10-n ≈ 6 x 10-n (1/Tanθ )

[edit] Induced Voltage

Induced Voltage is defined as the voltage of the turns which oppose the current flow


-ξ = N \frac{dB}{dt} = \frac{d\phi}{dt} where Φ = NB

[edit] Types of Inductors

[edit] Coil

For a straight wire with the following dimensions Length l, Area A, and Permitivity u and number of Turns N

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

[edit] Network

Inductors can be connected in series to increase inductance or in parallel to decrease inductance

[edit] Parallel Connection

A diagram of several inductors, side by side, both leads of each connected to the same wires
 \frac{1}{L_\mathrm{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots +  \frac{1}{L_n}


[edit] Series Connection

A diagram of several inductors, connected end to end, with the same amount of current going through each
 L_\mathrm{eq} = L_1  + L_2 + \cdots + L_n \,\!

[edit] Reference