## 5 c]For the single phase transformer obtain an expression for EMF induced in either primary side or secondary side.

**Solution :**

N1 – be the no. of turns of the primary winding

N2 – be the no. of turns secondary winding

f – Frequency in Hz

Φ – flux in weber

E1- be the RMS value of emf induced in the primary

E2 – be the RMS value of emf induced in the secondary

When the supply Voltage is applied to the primary winding which sets an alternating flux „

φ‟. Hence an EMF „E1‟ and „E2‟ are induced in the primary and secondary winding respectively

e=\frac{d\phi }{dt}-------(1)Consider a one cycle of EMF

Let us consider 1/4th cycle of EMF

The change in flux in 1/4^{th} cycle is

dφ= Φm – 0= Φm

The time taken to complete 1/4^{th} of cycle is

dt = 1/4f

Substituting dφ and dt in equation I we get

E_{avg}=\frac{d\phi }{dt}=\frac{\phi_{m}}{1/4f}= 4f\phi_{m}

we know that E_{rms} = 1.11 x E_{avg}

Therefore E_{rms} = 1 11 X 4 f Φ_{m}

E_{rms }= 4 44 f Φ_{m} induced per turn

If N1 be the number of turns in primary then E_{1}=4.44 f\phi_{m}N_{1} volts

If N2 be the number of turns in secondary then E_{2}=4.44 f\phi_{m}N_{2} volts