Motion Along a Straight Line at Constant

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Transcript Motion Along a Straight Line at Constant

Book Reference : Pages 130-132
1.
To understand that transformers are all
around us in everyday life
2.
To understand the significance of A.C.
3.
To be able to specify transformers using the
“transformer rule”
4.
To be able to complete efficiency calculations
In everyday life transformers are all around us :
We probably think of
them providing low
voltages from the
mains supply....
However they can
also produce high
voltages
1. Transformers make use of “scenario 2” a fixed
coil in a changing magnetic field (Must be A.C.)
2. Typically there are two coils (primary and
secondary) there is no electrical connection
between them
3. However, often the primary and secondary
coils are wrapped around the same iron core
4. Transformers can be used to “step up” the
voltage (make bigger) or “step down” the
voltage (make smaller)
When one side of the transformer is connected to an
A.C. supply an alternating magnetic field is produced in
that winding. The other side of the transformer sees this
as a changing flux linkage and an alternating EMF is
induced there.
When an alternating p.d. is applied to the
primary coil, let  be the flux passing through
each turn of the secondary coil
Flux linkage at the secondary is :
NS
where NS is the number of turns in the
secondary coil
From Faraday’s law the induced EMF in the
secondary is therefore
VS = NS / t
At the same time, the flux linkage at the primary
is :
NP 
where NP is the number of turns in the primary
coil
From Faraday’s law the induced EMF in the
primary is therefore
VP = NP / t
This EMF induced in the primary opposes the
original PD applied to the primary
Assuming negligible resistance all of the induced
primary EMF acts against the original applied p.d.
If we divide VS by VP we get
VS / VP = NS/t  NP/t
= VS / VP = NS / NP
(transformer rule)
In terms of voltage :
Step down transformer NS < NP  VS < VP
Step up transformer NS > NP  VS > VP
To make transformers as efficient as possible the
following design points are adopted :
1. Low resistance windings to reduce the power
lost due to the heating effect of current
2. A soft iron core is easily magnetised &
demagnetised
3. The core is laminated to reduce “Eddy
currents” (currents induced in the core itself).
This maximises the magnetic flux
Transformer efficiency =
Power delivered by the Secondary
Power delivered by the Primary
= ISVS / IPVP
x 100%
Assuming that losses are negligible
Power in the primary = Power in the secondary
or
IPVP = ISVS
rearranging for current ratio
VP / VS= IS / IP
From before NP / NS = IS / IP
In a :
Step down transformer voltage steps
down & the current is stepped up
Step up transformer voltage steps up &
the current is stepped down
Note opposite voltage to current relationship
Thinking about it, this has to be the case for
power (IV) (energy per second) to be conserved
A step down transformer reduces 230V to 12V. A 12V
48W lamp is connected to the secondary.
If the transformer has 1050 turns in the primary how
many turns are there in the secondary?
When the lamp is on the primary current is 0.22A.
Calculate the secondary current and the efficiency
Rewriting VS / VP = NS / NP
NS = NP VS / VP
for NS
= 1050 x 12 / 230 = 54 turns
Power supplied to lamp = ISVS = 48W
 IS = 48W / VS
= 48/12 = 4A
Transformer efficiency =
Power delivered by the Secondary
Power delivered by the Primary
Power delivered by the primary = VSIS
= 230 x 0.22
= 50.6W
Transformer efficiency
= 48 / 50.6
= 95%