Practical Electronics/Inductors

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[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

$X_L = \frac {L \frac{dI}{dt}}{I}$

$X L = ω L$ /_90
$X L = j ω L$
$X L = s L$

[edit] Impedance

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

$Z L = R L + X L$
$Z_L = \sqrt{R_L^2 + (\omega L)^2}$ /_Tan^-1 $\omega \frac{L}{R}$
$Z L = R L + j ω L$
$Z L = R L + s L$

[edit] Frequency Respond

Inductor is a device depends on frequency $ω$

$ω = 0, X L = 0$ , Inductor Closed circuit, I ≠ 0
$ω = 00, X L = 00$ , Capacitor Opened circuit, I = 0
$\omega = \frac{R_L}{L}$

X L = R L

,

Z_L = [(R_L]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 / CR_C 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 = $ω L R L$ = 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

$\frac{1}{L_\mathrm{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots + \frac{1}{L_n}$

[edit] Series Connection

$L_\mathrm{eq} = L_1 + L_2 + \cdots + L_n \,\!$

[edit] Reference

wikipedia Inductor