Inductors

An inductor is a wire coil usually wrapped around an iron core

Toroidal core

Self InductanceA coil can induce a voltage in itself !!!??

Predict what happens when the switch closes.

What happens when the switch opens?

An inductor is designed to oppose a changing current

This is because it can induce an EMF in itself. This is called Self

Inductance.

Increasing current

Causes increasing magnetic fieldCauses increasing flux through coilCauses induced EMF

Direction of EMF opposes current change

Increasing current

Induced EMF

Current Increasing

Self Inductance• A coil can induce a voltage in itself.

• L is called the self inductance

Self Inductance (L) is measured in henries (H)

tIL

t

coilin EMF

Circuit Symbol for inductor:Considering resistance:

• This induced EMF (or back EMF) opposes the increase in current, so the current rises…

SLOWLY

This is called Self Inductance

(The coil induces an EMF in itself)

current

timeClose switch

I = V/R

R is the ohmic resistance of the inductor L

R

current

Close switch

Back EMF

Close switch

tIL

coilin EMF

timeClose switch

Imax

LR

Meaning of time constant : The time taken for the current to increase to 63% of the maximum value.

0.63 Imax

LR

Larger inductance produces larger back EMF with the same change rate of magnetic flux as in . It opposes the EMF of the power supply, resulting in longer time to reach maximum current.

Larger resistance results in smaller maximum current. So it takes shorter time to reach 63% of the maximum current, resulting in smaller τ.

ΔtΔφLε

current

Close switch

How would the graph change if: Inductor had higher inductance? Inductor had higher resistance (be careful)

Time

Decreasing current

Causes decreasing magnetic fieldflux decreasing

Causes induced EMF

Direction of EMF opposes current change.

Current Decreasing

This induced EMF (or back EMF) opposes the decrease in current, so the current drops…

SLOWLY

This is called Self Inductance Key idea:• Inductors oppose a changing current

but have no effect on constant current.• n.b. a real inductor has resistance

When the switch opens, the current drops to zero rapidlyCauses a large flux change rate

Induces a very large EMF

Causes a spark across the switch

Energy stored in an inductor

Current in an inductor produces a magnetic field, therefore energy is stored in the magnetic field.

L: self inductance in henries (H),I: current in amps (A)

2

21 LIE

• Inductor radio

Example: As shown, the coil has an inductance of 0.20H. When the switch S is open, the current falls from 5.0A to zero in 1.0s.

a. What is the induced voltage?b. What is the resistance, R, of the coil c. What is the energy stored when S is closed?d. What is the time constant of the coil?

A0.5I 3.0V,V 0s,.1t 0.20H,L o

0.60Ω5.03.0

IVR b.

2.5J5.00.2021LI

21E c. 22

s33.00.600.20

RL d.

VV 0.11.0

5.00.20tIL a.

Ex. (a) What is the steady current flowing when the switch has been closed for a long time?(b). What is the voltage across the inductor at the instant the witch is closed?(c) find the time constant.(d)How long does it take for the current to reach a value of 0.021A?

Mutual Inductancehttp://

phet.colorado.edu/web-pages/simulations-base.html