# Basic Electrical Engineering (3110005)

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

## Q3) (b)

#### Derive the EMF equation of single-phase transformer.

• 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,
${\varnothing }_{\mathrm{m}}$ be the maximum value of flux in ${\mathrm{W}}_{\mathrm{b}}$
$\mathrm{f}$ be the supply frequency in $\mathrm{Hz}$
${\mathrm{N}}_{1}$ be the number of turns in the primary winding
${\mathrm{N}}_{2}$ be the number of turns in the secondary winding
$\varnothing$ 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 ${\mathrm{E}}_{1}$ is the emf induced in the primary winding.

Maximum valve of induced emf, Equation

;  Where,

RMS value is given by,

Putting the value of ${\mathrm{E}}_{1\left(\mathrm{max}\right)}$ in above equation. We get,

Similarly, We get,