Page 471 - Physics Coursebook 2015 (A level)

Chapter 29: Alternating currents
WORKED EXAMPLE
3 A radio requires a 6.0 V supply but has to be operated from a 230 V mains supply. It is fitted with a transformer to reduce the mains voltage. Calculate the turns ratio for this transformer. If the primary coil has 5000 turns, how many turns must the secondary have?
Step 1 The turns ratio Ns is given by:
Np Vs = Ns
Vp Np Hence:
Ns = Vs = 6.0 =0.026 Np Vp 230
This ratio is less than one because we are reducing the voltage.
Step2 WeknowthatNp=5000,sowecan calculate Ns.
Ns = Np × 0.026 = 5000 × 0.026 = 130
So the secondary coil must have 130 turns. Check that this seems reasonable: the voltage has to be reduced by a factor of about 40, so the number of turns must be reduced by the same factor.
Voltage, current, power
If there is no power lost in a transformer, it follows that the quantity I × V is the same for both primary and secondary coils: V I
IpVp = IsVs or Vs = Ip p s
In other words, the ratio of the voltages is the inverse ratio of the currents. If the voltage is stepped up, the current is stepped down, and vice versa. This explains the function of transformers in power transmission, as discussed earlier.
Note that this relationship assumes that no power is lost in the transformer. In practice, some power is lost because of the resistance of the transformer coil windings, so that the windings become warm. In addition, the changing magnetic flux can induce currents in the core. These eddy currents heat the core because of its resistance. Large transformers such as the one shown in Figure 29.14 handle a large amount of power. A small percentage is wasted, and the resulting heat is carried away by cooling fluid pumped around the transformer and through the fins which are visible in the photograph.
The transformers used in the electricity supply industry must be designed with great care to minimise energy
Figure 29.14 Installing a new transformer in a gold mine in Ghana.
losses. The electricity supply may pass through as many as ten transformers between the generator and the consumer. If each transformer wasted just 1% of the power, that would give an overall loss of 10%. Since there are roughly 100 big power stations in the UK, that would require ten power stations just to cope with the losses in transformers. Today’s well-designed transformers have losses of under 0.1%. This contributes greatly to energy savings in the power transmission industry.
QUESTIONS
13 A step-up transformer has a turns ratio of 10 : 1. When an alternating p.d. of 20 V is connected across the primary coil, a current of 50 mA flows init.
a Calculate the values of the p.d. across the secondary coil and the current flowing in it, assuming no power is lost in the transformer.
b In practice the secondary p.d. is found to be 180 V and the secondary current is 4.5 mA. What percentage of the power is wasted in the transformer?
14 Table 29.1 shows information about three transformers. Copy and complete the table. (Assume no power is lost in the transformers.)
Table29.1 DetailsofthreetransformersforQuestion14.
Transformer
Np
Ns
Vp/V
Vs/V
Ip/A
Is/A
P/W
A
100
500
230
1.0
B
500
100
230
1.0
C
100
12
240
0.2
459