# Electrical Transformer

**Definition:** The electrical transformer is a static device which consists of two or more stationary electric circuits interlinked by a common magnetic circuit for the purpose of transferring electrical energy between them. The transfer of energy from one circuit to another take place without a change in frequency.

## Construction and Working of an Electrical Transformer

Consider two coils 1 and 2 wounds on a simple magnetic circuit as shown in the figure. These two coils are insulated from each other, and there is no electrical connection between them. Let T_{1} and T_{2} be the number of turns in coils 1 and 2 respectively.

When a source of alternating voltage V_{1} is applied to coil 1, an alternating current I_{0} flows in it. The alternating current produced an alternating flux φ_{m} in the magnetic circuit. The means path of this flux is shown in the figure above by the dotted line. The alternating flux links the turns T_{1} of coil 1 and induces in them an alternating voltage E_{1} by self-induction.

All the flux produced by coil 1 also links T_{2} turns of coil 2 and induces in them a voltage E_{2} by mutual induction. If coil 2 is connected to load than an alternating current will flow through it, and the energy will deliver to the load.

The electrical energy is transferred from coil 1 to coil 2 by a common magnetic circuit. Since there is no relative motion between the coils, the frequency of induced voltage in coil 1 is the same as the frequency of the applied voltage to coil 1.

The coil 1 which receives the energy from the source of AC supply is called the primary coil or primary winding. Coil 2 which is connected to a load and delivers energy to the load, is called the secondary coil or secondary windings. The circuit symbol for the two windings transformer is shown in the figure below. The vertical bars represent the magnetic coupling between the windings.

### EMF Equation of an Electrical Transformer

The emf induced in each winding of the transformer can be calculated from its emf equation.

The instantaneous emf Induced in a coil of T turns linked by this flux is given by Faradays laws as

The above equation may be written as

where E_{m} = 4.44ωΦ_{m} = maximum value of e. For a sine wave, the r.m.s value of e.m.f is given by

The emf induced in each winding of the transformer can be calculated from its emf equation.Let subscripts 1 and 2 be used for primary and secondary quantities.The primary RMS voltage is

Where φ_{m} is the maximum value of flux in Weber (Wb), f is the frequency in hertz (Hz) and E_{1} and E_{2} in volts.

If, B_{m} = maximum flux density in the magnetic circuit in Tesla (T)

A = area of cross-section of the core in square meter (m^{2})

The winding with the higher number of turns will have high voltage and is called high voltage (HV) winding. The winding with the lowest number of turn is called low voltage (LV) winding.

### Voltage Ratio and Turns Ratio

The ratio of E/T is called volts per turn. The primary and secondary volts per turns is given by the formula

The equation (1) and (2) shows that the voltage per turn in both the winding is same, i.e.,

The ratio T_{1}/T_{2} is called the turn ratio.

The ratio of primary to secondary turn which equals to primary to secondary induced voltage indicates how much the primary voltage lowered or raised. The turn ratio or induced voltage ratio is called the transformation ratio, and it denoted by the symbol a. Thus,

The any desired voltage ratio can be obtained by shifting the number of turns.