Basic Electrical Engineering (3110005)

Question-3b-OR

BE | Semester-1 Winter-2019 | 11-01-2020

Q3) (b)

When a AC voltage is applied to the primary winding of a transformer, alternating flux sets up in the iron core of the transformer. This alternating flux links with both primary and secondary winding.
The function of flux is a sine function. The rate of change of flux with respect to time is derived mathematically.
Let,
$\emptyset_{m}$ be the maximum value of flux in $W_{b}$
$f$ be the supply frequency in $Hz$
$N_{1}$ be the number of turns in the primary winding
$N_{2}$ be the number of turns in the secondary winding
$\emptyset$ is the flux per turn (in Weber)
As shown in the figure that the flux changes from + to – in half a cycle of $\frac{1}{2}$ f second.
By Faraday’s Law of electromagnetic induction, Let $E_{1}$ is the emf induced in the primary winding.

$E_{1} = - N \frac{d \emptyset}{dt}$

Maximum valve of induced emf, Equation

E_{1 (\max)} = N_{1} ω \emptyset_{m}

E_{1 (\max)} = 2 π f N_{1} \emptyset_{m}

; Where,

ω = 2 π f

RMS value is given by,

E_{1} = \frac{E_{1 (\max)}}{\sqrt{2}}

Putting the value of

E_{1 (\max)}

in above equation. We get,

E_{1} = \sqrt{2} π f N_{1} \emptyset_{m}

E_{1} = 4.44 f N_{1} \emptyset_{m}

Similarly, We get,

E_{2} = 4.44 f N_{2} \emptyset_{m}