1. Transformers

2. Today’s lesson
• What is the purpose of transformers?
• What energy changes take place in a
transformer?
• How is the efficiency of transformers
improved by better design?

3. A typical set up...
Power
Station
P = 100MW
V = 25 KV
I = 4000 A
Step up
Transformer
Power Lines
P = 100MW
V = 400KV
I = 250 A
Step down
Transformer
Houses etc
P = 100MW
V = 240V
I = 420 000 A
(Many Houses!)

4. Resistance
Power
Station
P = 100MW
V = 25 KV
I = 4000 A
Step up
Transformer
Power Lines
P = 100MW
V = 400KV
I = 250 A
Step down
Transformer
Houses etc
P = 100MW
V = 240V
I = 420 000 A
(Many Houses!)
Power cable resistivity is very low but because of the long distances involved, it
begins to make a difference. The resistance from the local PowerStation to the
school would be roughly 100Ω.
Voltage lost = current x resistance (V = IR)
Without the transformer V = 4000 x 100
V = 400000V
With the step up transformer V = 250 x 100
V = 25000V
Voltage dropped
as heat

5. Step Down Transformers
There are transformers along the grid that slowly step down the voltage,
this is because heavy industry, light industries and homes need a
different voltage.
25 KV
275KV
132KV
11kV
5KV
230V230V

6. How does a transformer work?
There is a primary and secondary coil
What is the relationship between the ratio of the number coils and the ratio of the
voltages between the primary and secondary coil?
3V ac
Bulb 1
2 iron cores pushed together
Warning:
form a powerful electromagnet
Bulb 2
Primary Coil Secondary Coil
Primary coil Secondary coil
10 turns 20 turns
20 turns 10 turns
15 turns 30 turns
30 turns 15 turns
Bulb 1 Bulb 2

7. The Transformer Rule
Transformers consist of two coils, a primary and secondary
coil. When an AC current is connected to the primary coil
it produces a magnetic field in the iron core
The field cuts the secondary coil and induces an alternating current
Magnetic flux (Greek letter Φ (phi)), is a measure of the magnetic field
strength.
The transformer is designed so that all the magnetic flux from the primary coil
is transferred to the secondary coil
Flux linkage is a property of a coil of conducting wire and the magnetic field through
which it passes. It is determined by the number of turns of the coil (N) and the flux (Φ) of
the magnetic field.
The Flux linkage in the secondary coil = Ns Φ
NS is the number of turns in the secondary coil
The Induced emf in the secondary coil is equal to the rate of change of the
magnetic field. The stronger the field or the quicker the change in magnetic field
the greater voltage induced will be.
Vs = Ns d Φ
dt

8. = Np d Φ
dt
Similarly the voltage induced in the primary coil can be derived the same way
The applied voltage Vp opposes the induced voltage, assuming the coils have zero
resistance, the applied voltage equals the induced voltage
Vp = Np d Φ
dt
Dividing equation for Vs by the equation for Vp
Np d Φ
dt
Vs = Ns d Φ
dtVp
Vs = Ns
Vp Np
This is the transformer rule
Step up has more turns on the secondary coil. The voltage goes up and the
current goes down
Step down has more turns on the primary coil. The voltage goes down but the
current goes up

9. Transformer efficiency
To make transformers as near as 100% efficient
they have …
Low resistance windings to reduce heating
A laminated core consisting of iron separated by insulators to reduce eddy
currents in the metal core
A core of soft iron which is easily magnetised.
Efficiency = Power delivered by the secondary coil
Power supplied to the primary coil

10. 1. The needle kicks in one direction (say to the right) because as the current rises in
circuit 1, there is a change in magnetic flux. Some of this flux is linked with circuit 2,
inducing a current in this complete circuit.
2. No deflection as the flux is not changing when the current is constant.
3. The needle kicks in the opposite direction to question 1 as there is a flux change in
the opposite direction, i.e. flux is collapsing instead of growing.
4. The meter shows a steady deflection in ac mode.
5. The flux linkage between the coils is constantly changing due to the constantly
changing current.
6. Circuit B is more economical. In circuit B, current flows through the transformer
only when the bell push is pressed. In circuit A, current flows through the primary
circuit at all times, which wastes energy.
7. A large flux is linked due to the presence of the iron core and a very large number
of turns on the secondary winding. The contact is broken quickly, causing a large
change of flux in a short time. According to Faraday’s law, this produces a very
high voltage for a short time.

11. 8
(a)
Vs / Vp =Ns / Np , so Ns = (Np x Vs) / Vp. So (3000 X 9 V) / 230 V = 117.4
» 117 turns (nearest whole no.)
(b) Any two of the following:
Incomplete flux linkage between coils
Resistance of primary coil
Eddy currents induced in core
(c) With steady dc input the magnetic flux is constant so no emf will be induced
in the secondary coil