12-Introduction to Inductance and Inductors PDF

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Introduction to Inductance and Inductors

Online Resource for ETCH 213 Faculty: B. Allen

Self-inductance Self-Inductance – The property that causes a counterelectromotive force to be produced in a conductor when a magnetic field expands or collapses with a change in current.

Counter Electromotive Force (emf) – The voltage generated in an inductor due to alternating or pulsating current. It is always of opposite polarity to that of the applied voltage. Online Resource for ETCH 213 Faculty: B. Allen

Inductance Inductance - The property of a circuit or component to oppose any change in current as the magnetic field produced by the change in current causes an induced countercurrent to oppose the original change.

Henry – The unit of inductance.

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Inductor Inductor – A coil of conductor used to introduce inductance into a circuit. Factors determining Inductance: 1. Number of turns 2. Area of the coil 3. Length of the coil 4. Core material used within the coil Online Resource for ETCH 213 Faculty: B. Allen

Inductance is proportional to the number of turns. Inductance is proportional to the area of the coil. Inductance is inversely proportional to the length of the coil. Inductance in proportional to the permeability of the core. Online Resource for ETCH 213 Faculty: B. Allen

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N Aµ L= l L = Inductance in Henrys N = Number of turns A = Cross-sectional area of the coil in square meters µ = Permeability of the core material l = Length of the coil in meters Online Resource for ETCH 213 Faculty: B. Allen

Inductors in series LT = L1 + L2 + L3 + …

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Inductors in parallel LT =

1 1 1 1 + + + ... L1 L2 L3

For two inductors in parallel:

L1 × L2 LT = L1 + L2 Online Resource for ETCH 213 Faculty: B. Allen

Inductors in parallel

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Types of inductors Fixed-Value Inductors Air Core Iron Core Ferrite Core Variable-Value Inductors Online Resource for ETCH 213 Faculty: B. Allen

Fixed-value inductors Fixed-Value Inductor – An inductor whose value is fixed. Air-Core Inductor – An inductor that has no metal core. Iron-Core Inductor or Choke – An inductor used to impede the flow of alternating or pulsating current. Ferrous – Composed of or containing iron. A ferrous metal exhibits magnetic characteristics as opposed to nonferrous metals. Ferrite – A powered, compressed and sintered magnetic material having high resistivity. The high resistance makes eddy-current losses low at high frequencies. Online Resource for ETCH 213 Faculty: B. Allen

Variable-value inductor An inductor whose value can be varied

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Inductive time constant

L τ= R

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DC current fall

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AC current rise and fall

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Inductive reactance (XL) Inductive Reactance (XL) – Measured in ohms, it is the opposition to alternating or pulsating current flow without the dissipation of energy.

XL = 2 π f L f = frequency in hertz L = inductance in henrys Online Resource for ETCH 213 Faculty: B. Allen

Voltage in series RL circuits VR = I × R VL = I × XL

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Impedance in series RL circuits Z = V/I

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Phase shift in series RL circuits XL θ = arctan R

VL θ = arctan VR

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Power in series RL circuits Purely inductive circuit

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Quality Factor Quality Factor – The quality factor of an inductor or a capacitor is the ratio of a component’s reactance (energy stored) to its effective series resistance (energy dissipated).

Quality

Factor

(Q ) =

Energy Energy

Q=

XL R

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Stored Dissipated

Power in an RL circuit

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Power Factor True PF =

(PR ) Power (PA )

Power

Apparent or

PF = R/Z or PF = cos Online Resource for ETCH 213 Faculty: B. Allen

Current in parallel RL circuits

VS IR = R

VS IL = XL

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Phase angle in parallel RL circuit

IL θ = arctan IR

θ = arctan

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R XL

Impedance in a parallel RL circuit

VS Z= IT

Z=

R× XL 2

R +X Online Resource for ETCH 213 Faculty: B. Allen

2 L

Applications of inductors RL Filter – A selective circuit of resistors and inductors that offers little or no opposition to certain frequencies while blocking or attenuating other frequencies.

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RL Integrator – An RL circuit with an output proportional to the integral of the input signal.

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RL Differentiator – An RL circuit whose output voltage is proportional to the rate of change of the input voltage.

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End of Inductance and Inductors

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