6.4 More detailed notes explaining the theory and structure of transformers

See Part 6.6 for Examples of transformer calculations

A transformer is a device that can change the potential difference (p.d.) of an alternating current (a.c.)

It is another example of electromagnetic induction - the effect of magnetic fields inducing an ac current in a coil.

Transformers are nearly 100% efficient - important in the context of the National Grid electricity supply.

A basic transformer consists of two coils of insulated wire, a primary coil and a secondary coil independently wound on an iron core - see the diagram further down.

The wire is usually made of copper with a thin coating of insulation material.

Iron is used as because it is easily temporarily magnetised.

Both coils MUST consist of complete, but separate circuits - no electrical connection between them.

When an a.c. p.d. is applied across the primary coil, the iron core magnetises and demagnetises quickly due to the nature of the alternating current.

Therefore an alternating current (a.c.) in the primary coil (p) of a transformer automatically produces a alternating (changing) magnetic field in the iron core and hence in the secondary coil (s) by induction.

This induces an alternating potential difference across the ends of the secondary coil (V_s).

If the secondary coil is part of a complete circuit, an induced current will flow in the secondary coil.

Remember, the current MUST BE ac to get an alternating magnetic field that 'cuts' through the iron core', otherwise continuous induction will NOT take place.

Using a  d.c. current is no good - you don't get a constantly changing magnetic field if the current only flows one way!

KEY to transformer diagram:

V_p = p.d. across the input primary coil

V_s = induced p.d. generated across the output secondary coil

n_p = number of wire turns on the primary input coil

n_s = number of wire turns on the secondary output coil

I_p = input current flowing through the primary coil

I_s = induced output current flowing out through the secondary coil

A step-up transformer increases the p.d. and has a greater number of coils in the secondary coil than the primary.

A step-down transformer reduces the p.d. and has a smaller number of coils in the secondary coil than the primary.

For example, the images above illustrate the local electricity supply to some farms in a rural area using small-scale step-down transformers.

If you know the input p.d. and the number of turns on each coil, you can calculate the output p.d. using the equation below.

Subscript p is form the primary coil and subscript s for the secondary coil.

The ratio of the potential differences across the input primary coil and the output secondary coil of a transformer, V_p and V_s, depends on the ratio of the number of turns of wire on each coil, n_p and n_s and is given by a simple ratio equation. The data is 'pictured' on the diagram above.

Vp		np
----	=	----
Vs		ns

v_p / v_s = n_p / n_s   The p.d. and coils transformer equation

the ratios are the same i.e. input p.d. / output p.d = turns on primary coil / turns on secondary coil

and the potential differences, V_p and V_s in volts, V

In a step-up transformer V_s > V_p

In a step-down transformer V_s < V_p

See the diagram above for a visual appreciation of the equation.

 

If transformers were 100% efficient, the electrical power output would equal the electrical power input.

V_s × I_s = V_p × I_p    The transformer power equation

(remember power P = I x V, P in watts, W   and   I current in amps, A)

where    V_s × I_s     equals the power output from the secondary coil (never 100% efficient)

and       V_p × I_p     equals the power input to the primary coil

 

However, no transformer is ever 100% efficient, so the power output never equals the power input, because there are always energy losses eg as thermal (heat energy) - remember that the two coils of wire in a transformer are still acting as resistances, so there will always be a little energy change of electrical energy to thermal energy.

See Part 6.6 for Examples of transformer calculations