Transformers Elliott

We can use a magnetic field to induce a voltage in two ways: 1. Relative movement.  The size of the voltage depends on: Speed the magnet passes through a coil or vice versa. Number of turns in the coil. Strength of the magnet. 2.  Changing a magnetic field.  We don’t have to make the magnetic field move.  If we turn the current on or off, there is a change in the magnetic field, and that induces a voltage in a second unconnected coil.  T his is called the transformer effect or mutual induction.

What Are Transformers? Very simple machines: It consists of: A primary coil connected to the alternating power source.  This provides the changing magnetic field. A secondary coil connected to the load. A laminated soft iron core. The two coils are electrically completely different circuits.  Either of the coils can act as a primary. 

The Core The laminated core is made up of layers of soft iron separated by an insulating layer of varnish or glue. This reduces losses from eddy currents. Soft iron is NOT soft like putty; it is heavy and hard. However "soft" means that it loses its magnetism immediately the current is turned off. Therefore the magnetic field can change forwards to backwards as the current changes.

Input/Output Voltage The ratio of the input voltage to the output voltage is the same as the ratio of the number of turns on the primary to the number of turns on the secondary.  We can write this as:

Step Up / Step Down? If N1 is greater than N2, we have a step-down transformer, because the voltage is reduced. A step-up transformer increases the voltage. Therefore we can say that when the voltage is lower, the current is bigger.  We can rewrite the transformer equation in terms of current to give us: If a transformer is 100 % efficient (and it nearly is) we can say that:

In Reality In practice, the transformer is about 97 % efficient.  When a large transformer is transferring a lot of energy, even 3 % losses produce a fair amount of heat.  Therefore the transformer is cooled with oil which is pumped to heat exchangers.

Check Your Progress A power station generator generates 500 MW at a voltage of 15 000 V.  Assuming it to be single phase. (a) What is the current? (b) The voltage is stepped up to 275 000 volts.  Assuming that the transformer is 100 % efficient, what is the current in the secondary? (c) What is the turns ratio in the transformer?

Answer

Sources of Inefficiency The coils will have a certain value of resistance.  If the currents are large, the energy loss is large, since P = I2R. With the laminated soft iron core, there are still eddy currents, even though they are much reduced.  These will heat up the core.

Energy Loss Through Hysteresis Work has to be done in building up the magnetic field in the core.  It takes energy to line up all the domains.  The energy recovered as the magnetic field falls is less than what is put in. This is called hysteresis. The area within the loop is the energy lost. All magnetic materials have a certain remanance, meaning that the material is magnetised, even when the current is zero.  In soft iron, the remanance is low. There is a value of current at which all the tiny molecular magnets are lined up.  The magnetic field cannot increase further.  This is called saturation. 

Important Transformers can only work with alternating current; they cannot work with direct current. 

Check Your Progress A transformer has a primary of 3600 turns and a secondary of 150 turns.  It takes 1.5 amps from the 240 V mains.  (a) What is the turns ratio? (b) What is the output voltage and current?

Answer

Check Your Progress Transformers are very efficient machines, but are not 100 % efficient.  The best efficiency for a large power station transformer is about 97 %.  Outline the reasons for this and discuss whether there is a limit to the power input and output of such a transformer. A large industrial transformer steps an input voltage of 132 kV to an output voltage of 1000 V to provide power to an electric arc furnace.  The furnace takes a current of 40 000 amps.  The transformer is 95 % efficient.  Assume the current is single phase. (a) Calculate the power taken by the furnace. (b) Calculate the input current. (c) Calculate the power lost when the furnace is running. (d) Suggest how the lost power is removed from the transformer to avoid damage due to overheating.

Answer Q1 The energy losses arise from: Resistance in the coils.  If the currents are large, the power loss can become large, as the heating effect is governed by P = I2 R;  Eddy currents in the laminations of the core.  These are reduced by lamination, but not stopped altogether; Work needs to be done to build up the magnetic field in the core.  Not so much work is got out when the domains randomise again.  This is called hysteresis. The magnetic material has a certain amount of remanance, which means that some domains are still lined up even when there is no current in the coil.  This is true, even if the remanance is low, such as in soft iron. At a certain current level, all domains are lined up.  The magnet is saturated, and cannot become more magnetised.  Therefore a greater current will not pass across to the secondary coil.

Answer Q2