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11
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The rod is moving from left to right
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If the north pole of a magnet is suddenly thrust through a looped conductor, a current is created
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Current direction depends on which direction the magnet is being moved through the loop
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Topic 11 Page 2

Magnetic Flux
A current is created as a result of the motion of the magnet relative to the coil
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The galvanometer changes when:
• The relative speed of the magnet and the coil changes
• The strength of the magnet changes
• The number of turns changes
• The area of the loop changes
• The magnet moves at right angles to the plane of the loop

The magnetic flux is the product of the component of the magnetic field strength normal to an area
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the unit of magnetic flux is the weber (WB) or 1 T m 2
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If
a magnet is moved in the same plane as the loop, then the magnetic field lines do not pass through the loop
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The induced emf depends on the relative orientations of the B-field and area
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There are three ways to change the flux
1
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Change the area A
3
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Faraday found that th e induced emf is
equal to the (negative) rate of change of magnetic flux linkage
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In time

will move a distance of


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Topic 11 Page 4

Lenz's law
Lenz's law states that induced current will have a direction such that it will oppose the change in flux that produced it
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Lenz's law is much like energy conservation
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Use the right hand rule and configure your hand so you can see the current's direction (either clockwise or counterclockwise)
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There will be an emf induced in the loop as the flux is changing
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The loop will produce a magnetic field out of the
page to oppose the increase in flux
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Topic 11 Page 5

11
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A coil is made to rotate in a region of magnetic field
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The slip rings touch carbon brushes that transfer the current into an external circuit
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1
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Increase the flux change
3
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A sinusoidal pattern emerges
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The peak voltage is when
The emf induced is zero whenever the flux assumes its maximum or minimum values
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Alternating voltage is voltage that can be negative as well as positive
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Unlike direct current (dc) that flows
in a circuit connected to a battery, the electrons oscillate back and forth with the same frequency as that of the voltage
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The peak value

is given by the product of the peak voltage and peak current
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For alternating current (ac):

Topic 11 Page 8

RMS
The way to find the average of a regularly alternating voltage is called the root mean square
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The reason for using the rms values for AC current and voltage is that power consumption doesn't depend on the peak voltage (and peak current); rather, it depends
on the rms values, since they are an average
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In AC circuits there are components called capacitors and inductors which change the
phase relationship between and
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Here is how it works: the input coil, called the primary winding, is wrapped around a soft iron core
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The primary coil has
turns of wire and the secondary coil has turns
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The flux changes because the magnetic fields in both of the coils is changing
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The purpose of the iron core is to ensure that much of the flux produced in the primary coil as possible enters the secondary coil
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Because of flux linkage we know that for each winding the voltage is proportional to the number of loops
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Eddy currents are tiny currents created in the core because the free electrons of the core move in the
presence of a magnetic field
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Eddy currents can be minimized by lamination of the transfrormer core
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The heating of the coils themselves creates further losses of energy
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For real transformers there are eddy currents and hysteresis currents, both of which are created by Faraday's law due to the magnetic flux change that is naturally a part of
AC circuits
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Hysteresis losses are less signficant than eddy losses
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A city will have a power demand of
stations sends out electricity at a voltage and a current flows in the cables from the power station then:

which is quite large
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Since
, if we want to minimize we can increase V, maintaining the power that is to be delivered
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Transformers are used to reduce the high voltage down to that required for normal household appliances
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Topic 11 Page 11

Diode bridges and rectification
It might be necessary to convert an ac current into a dc current (a current where the electrons all flow in the same direction)
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The conversion from AC to DC is called rectification
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Its schematic symbol shows the direction of the conventional (+) current flow
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This is half-wave rectification
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Full-wave rectifier
A better way to rectify is with a diode bridge rectifier
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In the next half
cycle, the current is counter-clockwise
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If we supply an AC input to the diode "bridge" there will always be a path for a lobe to make it through and produce a DC voltage drop across the load
resistor
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No matter what the polarity of the supply terminals, the top
output will be (+) and the bottom output will be (-), thus we have DC at the output
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It varies from 0 to V twice in each period
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This problem can be corrected simply by adding a large-valued capacitor across the output
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Topic 11 Page 12

11
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It is made up of two parallel plates separated by an insulating material or a vacuum
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Capacitance is defined as the charge per unit voltage that can be stored on the capacitor
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is the charge per unit voltage in Coulombs (C)
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Capacitance depends on the geometry of the capacitor
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Dielectric materials
In parallel plates, the electric field is directed from top to bottom (from to )
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This polarises the
electrons and creates an electric field in the opposite direction of the electric field of the plates
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The net electric field (electric force) between the parallel plates is reduced
compared to that in a vacuum
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The capacitance increases when there is a dielectric, because
there is more charge
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There are two ways to increase capacitance
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Increase the area over which charge can be stored
2
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Topic 11 Page 15

Capacitance Connection
Capacitance - parallel
The capacitors are in parallel, so

Capacitance - series
The capacitors are in series so,

(These formulas are the reverse of those for resistance)

Topic 11 Page 16

Energy stored in a capacitor
Energy stored in a capacitor:

Topic 11 Page 17

Charging a capacitor

If the switch is moved to position A, the capacitor will charge
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When the switch is moved to A, the charge on the capacitor plates will increase
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38 the current is clockwise, meaning that the current is counter-clockwise
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The potential difference across the capcaitor plates will become equal to the emf of the battery
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The charge will eventually reach zero
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The quantity RC is called the time constant and is denoted by the symbol
and
The time constant determines the time scale for the discharge of the capacitor
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The time constant is the time after which the charge decreases to about
of its initial value
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The time constant is the time needed for the charge to decrease to half its initial value, divided by


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The half life of the capacitor is the time it takes for chage to decrease to half its initial value

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