Practical Electronics/Inductors

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[edit] Inductor

This device generates a magnetic field as current passes through it similar to the magnetic field of a magnet. An inductor stores electrical energy in the form of a magnetic field.

[edit] Inductor's Symbol

The symbol for inductance is L and is measured in Henry which has the symbol H.

[edit] Inductor's Construction

An inductor is a device made from a wire conductor with several turns that has the dimensiion permability, length of inductor, and number of turns and inversely proportional to cross-sectional area.

$L = \frac{B}{I}$ = μN^2 $\frac{A}{l}$

[edit] Characteristics

[edit] Inductance

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

$L = \frac{B}{I}$

[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] 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

$f = \frac{Tan\theta}{2\pi}\frac{R_L}{L}$
$t =\frac{2\pi}{Tan\theta}\frac{L}{R_L}$

[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] Từ Dung

Từ Dung là tính chất Vật lý của Cuộn Từ đại diện cho Từ Lượng sinh ra bởi một Dòng Điện trên Cuộn Từ . Từ Dung đo bằng đơn vị Henry H và có ký hiệu mạch điện L

$L = \frac{B}{I}$

Cuộn Từ tạo từ một cộng dây dẩn điện có kích thứớc Chiều dài , l , Điện tích , A , với vài vòng quấn N . Khi mắc với điện

$L = \mu N^2 \frac{l}{A}$

Độ Dẩn Từ của vật liệu

$\mu = \frac{B}{I} \frac{A}{l} \frac{1}{N^2}$

Construction	Formula	Dimensions
Cylyndrical Coil ^[1]	$L=\frac{\mu_0KN^2A}{l}$	L = inductance in henries (H) μ₀ = permeability of free space = 4 $π$ × 10^-7 H/m K = Nagaoka coefficient^[1] N = number of turns A = area of cross-section of the coil in square metres (m²) l = length of coil in metres (m)
Straight wire conductor	$L = l\left(\ln\frac{4l}{d}-1\right) \cdot 200 \times 10^{-9}$	L = inductance (H) l = length of conductor (m) d = diameter of conductor (m)
Straight wire conductor	$L = 5.08 \cdot l\left(\ln\frac{4l}{d}-1\right)$	L = inductance (nH) l = length of conductor (in) d = diameter of conductor (in)
Short air-core cylindrical coil	$L=\frac{r^2N^2}{9r+10l}$	L = inductance (µH) r = outer radius of coil (in) l = length of coil (in) N = number of turns
Multilayer air-core coil	$L = \frac{0.8r^2N^2}{6r+9l+10d}$	L = inductance (µH) r = mean radius of coil (in) l = physical length of coil winding (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Flat spiral air-core coil	$L=\frac{r^2N^2}{(2r+2.8d) \times 10^5}$	L = inductance (H) r = mean radius of coil (m) N = number of turns d = depth of coil (outer radius minus inner radius) (m)
Flat spiral air-core coil	$L=\frac{r^2N^2}{8r+11d}$	L = inductance (µH) r = mean radius of coil (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Toroidal core (circular cross-section)	$L=\mu_0\mu_r\frac{N^2r^2}{D}$	L = inductance (H) μ₀ = permeability of free space = 4 $π$ × 10^-7 H/m μ_r = relative permeability of core material N = number of turns r = radius of coil winding (m) D = overall diameter of toroid (m)