# Transformer

What is the Transformer?

A transformer is an electrical device that can change the voltage in an ac electric circuit.

We can find the transformer in various devices/items at our homes, which are:

1. The stabilizer at our homes has an inbuilt transformer,

2. Inside the mobile charges.

A transformer can transform a high voltage to low voltage, and vice versa.

There are two types of transformers, which are:

1. Step-up transformer

2. Step-down transformer

If a transformer increases the ac voltages, then it is called the step-up transformer, and if it decreases the ac voltages, then it is called the step-down transformer.

You may have seen the step-up transformers in a power station.

The power stations supply a very high voltage in our area, the step-down transformer decreases this voltage, and we get this voltage at our homes.

Transformers operate only on the alternating current.

Working Principle of the Transformer

The transformer operates on the principle of mutual induction.

Construction of the Transformer

A transformer consists of a ferromagnetic material, i.e., a rectangular soft iron core made of laminated sheets, well insulated from one another.

We wound the two coils primary coil and the secondary coil on the same core, as shown in the diagram below:

So, in the primary coil, the number of turns of wire is NP and NS in the secondary coil.

We use copper wires in the tight windings of P and S coil.

If we look at this diagram, NP > NS. However, this may not always be true. The reverse can also be true.

Now, we connect the source of alternating emf to the P coil and the load resistance R to the S coil through an open switch O, as shown in the diagram below:

The switch is open, so no current flows. Now, let us close the switch and get our complete circuit.

This is our final construction, i.e., transformer

Now, let us see the working on the transformer.

We can see that the windings of the coils are similar to the solenoid.

On supplying input voltage or current to the P coil, a magnetic field generates in it, which is in an upward direction.

In an ideal transformer, all these magnetic field lines go into the S coil and revert to the P coil, as you can see in diagram a. This reverting is because of the ferromagnetism of the soft iron core, i.e., it allows the passage of the magnetic field lines.

We know that changing current creates a changing magnetic flux. According to Faraday’s law, the change in flux gives rise to an induced emf, which is given by

E = dф/dt

Now, let us calculate the flux in both the coils (considering the area of both the coils as A)

The flux in each turn of the primary coil = ф

Similarly, for the secondary coil = ф

This means if a unit flux flows in the P coil, the same flux passes through the S coil.

So, the total flux in P with NP turns  =  фPNP, and for S coil = фSNS

The induced emf for P, i.e., EP = - NP d(фP)/dt…(1), and

For S coil, ES=  - NS d(фS)/dt….(2)

(2) (1)

 $\frac{E_{S}}{E_{P}}$ = $\frac{N_{S}}{N_{P}}$

This means an induced emf is directly proportional to the number of turns. Wherever the voltage is high, the emf induced is also higher.

Here, $\frac{Ns}{Np}$ = K represents the transformation ratio.

Conditions for constructing two types of transformers

Step-up Transformers

If we wish to construct a step-up transformer, i.e.,  we want to increase the output voltage, then the conditions are:

1. ES > EP

For getting a higher voltage, the emf of the secondary coil must be greater than the emf of the primary.

1. NS > NP

The number of turns in the secondary coil should also be greater than the number of turns in the primary coil.

Step-down Transformers

If we wish to construct a step-up transformer, i.e., we expect the lower output voltage. Therefore, we need to decrease the ac voltage.

Then conditions for constructing step-down transformers are:

1. ES < EP

For getting a lower ac voltage supply at our homes, the emf of the secondary coil must be lesser than the emf of the primary.

1. NS < NP

The number of turns in the secondary coil should also be lesser than the number of turns in the primary coil.

The Efficiency of a Transformer

The efficiency of a transformer is the ratio of output power to the input power and is denoted by η.

So, the rate at which a source transfers energy (provides input power) to the primary coil is equal to EPIP.

The rate at which the transformer provides the output power = ESIS.

So, the formula for the efficiency of a transformer is:

 η = $\frac{E_{S}I_{S}}{E_{P}I_{P}}$

For an ideal transformer, ESIS = EPIP, or  η =1 (i.e., 100%)

Q1: A Transformer has an Efficiency of 60%. It Works at 5 kW and 100 Volt. If the Secondary Voltage is 240 V, Find the Primary and Secondary Currents.

Ans: Here, η = 60%, Pi = 4 kW = 4000 W, EP = 100 V, ES = 240 V, IP = ?, IS = ?

As Pi = EPIP IP = Pi/EP = 40 A

η = EsIs/EpIp ⇒ 60/100 = 240IS/4000

On solving, we get IS = 10 A

So, the values are:

 IS = 10 AIP = 40 A

Q2: How Much Current is Drawn by the Primary Coil of the Transformer that Steps Down the Voltage from 220 V to 24 V to Operate a Device with an Impedance of 240 Ohms?

Ans: Here, EP = 220 V, ES = 24 V, RS = 240 ohm, IP = ?

We know that IS = ES/RS = 24/200 = 0.12 A

As  IP = IS  * Es/Ep

= 0.12 * 24/220 = 0.0131 A

Q3: The Number of Turns in S Coil is 600 Times that in the Primary. What Power is Obtained from Secondary When Pi = 10 W?

Ans: Here, NS > NP, and Pi = 10 W

The output power must be 10 W at the most, provided that there is no power loss.

Q4: Write the Name of Three Types of Voltage Transformers.

Ans: The three types of voltage transformers are:

1. Electromagnetic,

2. Capacitor, and

3. Optical voltage transformer.