# Ideal Transformer Example

An idea transformer has a 275-turn primary and 825-turn secondary. The primary is connected to a 200-V, 60-Hz source. The secondary supplies a load of 5 A at a lagging power factor of 0.5. Find the turns-ratio, the current in the primary, the power supplied to the load, and the flux in the core.

## Contents

### Solution

(A) $\ {turns-ratio}=\frac{N_{1}}{N_{2}}$ $\ =\frac{275}{825}$ $\ =0.333$

(B) Because $\ {I_{2}}=5 A$, the current in the primary is...

$\ {I_{1}}=\frac{I_{2}}{turns-ratio}$ $\ =\frac{5}{0.333}$ $\ =15 A$

(C) $\ {V_{2}}=\frac{V_{1}}{turns-ratio}$ $\ =\frac{200}{0.333}$ $\ =600 V$

Therefore, the power supplied to the load is...

$\ {P_{L}}=V_{2} I_{2}\cos(\theta)$ $\ =600 * 5 * 0.5$ $\ =1500 W$

(D) $\ {\phi_{m}}=\frac{E_{1}}{4.44 f N_{1}}$ $\ =\frac{V_{1}}{4.44 f N_{1}}$ $\ =\frac{200}{4.44 * 60 * 275}$ $\ =2.73 mWb$

## Reviewers

Aric Vyhmeister

Erik Biesenthal

The way to do capital phi, $\ \Phi$, for the flux is to capitalize the first letter of the word, i.e. \Phi instead of \phi. And if you want a space between the number and the units, space is \(space), as in "\ ".