For the single phase transformer obtain an expression for EMF induced in either primary side or secondary side

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