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UPRVUNL JE EE 2014 Official Paper

Option 1 : E_{1} = 4.44 f P_{M} N_{1}

ST 1: General Knowledge

5966

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**E.M.F. Equation of a Transformer:**

Consider,

N_{1} = No. of turns in the primary

P_{M} = Maximum flux in core in Wb

f = Frequency of AC input in Hz

The flux increases from its zero value to maximum value P_{m} in one-quarter of the cycle as shown.

Note: The rate of change of flux per turn means induced EMF in volts.

The average rate of change of flux (E_{a}) per turns is given as,

\({E_a} = \frac{{{\rm{\ P_m }}}}{{\frac{{{\rm{\ 1 }}}}{{4f}}}}=4fP_M\)

If flux p is the instantaneous value of flux varies sinusoidally, then RMS. value of induced EMF is obtained by multiplying the average value with the form factor.

The form factor of a sinusoidal wave is 1.11

RMS value of EMF (E_{r}) = 1.11 × average value of EMF (E_{a})

E_{r} = 1.11 × 4 f P_{M}

E_{r} = 4.44 f P_{M}

If primary winding has N_{1} number of turns then primary RMS induced voltage (E_{1}) is given as,

**E1 = 4.44 f PM N1**