INDUCTANCE

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DEFINED

When a length of wire is formed onto a coil, it becomes a basic inductor

DEFINED

Magnetic lines of force around each loop in the winding of the coil effectively add to the lines of force around the adjoining loops, forming a strong electromagnetic field within and around the coil

DEFINED

A inductor is a device which stores energy in a magnetic field

DEFINED

Inductor consists of a coil of wire, usually around a metallic or ferromagnetic core which creates an electromagnet

DEFINED

A current through an inductor creates a magnetic field around the coil which resists any changes in current

DEFINED

The unit of inductance is the henry (H), defined as the inductance when one ampere per Second through the coil, induces one volt across the coil

l

ANL

2

DEFINED

The unit of inductance is the henry (H), defined as the inductance when one ampere per Second through the coil, induces one volt across the coil

l

ANL

2

N= Number of Turnsµ = dielectric constantA = cross-sectional area of the coill = length of the coil

DEFINED

Schematic Symbols

Fixed Inductor Variable

• A couple of symbols for the inductor are illustrated below

L1

1.0mH

L2

10mH-VARKey = A

50%

INDUCTOR TYPES

Toroidal core inductor Axial Lead Variable Inductor

Rules of Inductor Behavior

The current and voltage relationship in an inductor is

If the current isn’t changing, then the voltage change across the inductor is zero

t

iL

dt

diLtv

)(

Rules of Inductor Behavior

An inductor is a short circuit to DC The current through an inductor cannot

change instantaneously If current changed quickly, then we might

have infinite voltage Contradicts conservation of energy

t

iL

dt

diLtv

)(

Example Problem 1What are the values of I and V, the current through and voltage across the inductor?

The easier value to find is the voltage V. In this case, the current through the inductor isn’t changing, so the voltage must be 0 V. So V = 0 V

In DC conditions, an inductor acts like a short circuit – so we need to find the current through the resistor and it will be the same as the current through the inductor.

mAk

V

R

VI 5

1

5

INDUCTOR CODEUse the color code guide in your handout as a means to

Identify the value of the inductor.

RL TIME CONSTANT

The RL Time Constant is the time it takes, in a series resistor inductor circuit, for current to rise to 63.2% or fall to 36.8% of the peak voltage value of the circuit. When five of these time constants occur, the inductor will be fully discharged. The formula below can be used to predict this value.

RLt / t = Time in secondsR = Resistance in OhmsL = Inductance in Henry’s

RL TIME CONSTANT

The current across an inductor cannot change instantaneously because a finite time is required to move charge from one point to another (limited by circuit resistance)

RLt / t = Time in secondsR = Resistance in OhmsL = Inductance in Henry’s

RL TIME CONSTANT example

With a 1kΩ resistor and a 1mH inductor are placed in series, what is the time constant of the circuit and how long will it take to fully discharge the inductor?

Discharge Time = 1us x 5Full Charge Time = 5us

Time for DischargeTime Constant Calculationt =L/Rt=1mH/1kΩ t =.001/1000t=1us

The first cursor proves that at 1us the current is 6.32V

The second cursor is showing that after 5 time constants the inductor represents a short circuit.

RL TIME CONSTANT GRAPHIC REPRESENTATION

When a DC voltage source is connected to the inductor, voltage is maximum across the inductor because of the magnetic field caused by the maximum rate of change of current in the circuit.

Note: at t = 0 seconds •Current is 0 Amps•Voltage is Maximum Volts

THEORY

/tEeVL

)1( /)0(

teII tL

THEORYAs the magnetic field “relaxes” due to the continuous DC, current begins to flow through the inductor. When this occurs, the voltage across the inductor begins to decrease and current through the inductor begins to rise.

/tEeVL

)1( /)0(

teII tL

THEORYEventually the inductor represents a short circuit. In an ideal inductor the voltage drop becomes 0 Volts and the current through the inductor becomes maximum.

Note: at t = infinity seconds •Current is Maximum Amps•Voltage is 0 Volts

/tEeVL

)1( /)0(

teII tL

Series and Parallel Inductors Inductors in Series

With several Inductors in series, they all act together to affect the current

neq LLLLL ...321

Series and Parallel Inductors Inductors in Parallel

With several Inductors in parallel, we have to split the current, just like in resistors

neq LLLLL

1...

1111

321

End of Presentation