Question

Derive Emf equation of transformer

Answer 1

Answer:

the answer is

Explanation:

N1 = Number of turns in primary winding

N2 = Number of turns in secondary winding

Φm = Maximum flux in the core (in Wb) = (Bm x A)

f = frequency of the AC supply (in Hz)

emf equation of transformer

As, shown in the fig., the flux rises sinusoidally to its maximum value Φm from 0. It reaches to the maximum value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).

Therefore,

average rate of change of flux = Φm /(T/4) = Φm /(1/4f)

Therefore,

average rate of change of flux = 4f Φm ....... (Wb/s).

Now,

Induced emf per turn = rate of change of flux per turn

Therefore, average emf per turn = 4f Φm ..........(Volts).

Now, we know, Form factor = RMS value / average value

Therefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn = 1.11 x 4f Φm = 4.44f Φm.

RMS value of induced emf in whole primary winding (E1) = RMS value of emf per turn X Number of turns in primary winding

E1 = 4.44f N1 Φm

Answer 2

Answer:

Let,

N1 = Number of turns in primary winding

N2 = Number of turns in secondary winding

Φm = Maximum flux in the core (in Wb) = (Bm x A)

f = frequency of the AC supply (in Hz)

emf equation of transformer

As, shown in the fig., the flux rises sinusoidally to its maximum value Φm from 0. It reaches to the maximum value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).

Therefore,

average rate of change of flux = Φm /(T/4)    = Φm /(1/4f)

Therefore,

average rate of change of flux = 4f Φm       ....... (Wb/s).

Now,

Induced emf per turn = rate of change of flux per turn

Therefore, average emf per turn = 4f Φm   ..........(Volts).

Now, we know,  Form factor = RMS value / average value

Therefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn =  1.11 x 4f Φm = 4.44f Φm.

RMS value of induced emf in whole primary winding (E1) = RMS value of emf per turn X Number of turns in primary winding

         E1 = 4.44f N1 Φm          ............................. eq 1

Similarly, RMS induced emf in secondary winding (E2) can be given as

         E2 = 4.44f N2 Φm.          ............................ eq 2

from the above equations 1 and 2,

emf equation of transformer

This is called the emf equation of transformer, which shows, emf / number of turns is same for both primary and secondary winding.

For an ideal transformer on no load, E1 = V1 and E2 = V2 .

where, V1 = supply voltage of primary winding

           V2 = terminal voltage of secondary winding

Voltage Transformation Ratio (K)

As derived above,

voltage transformation ratio

Where, K = constant

This constant K is known as voltage transformation ratio.

If N2 > N1, i.e. K > 1, then the transformer is called step-up transformer.

If N2 < N1, i.e. K < 1, then the transformer is called step-down transformer.