Ideal Transformer Example

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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.

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

Author

Kyle Lafferty

Reviewers

Aric Vyhmeister

Erik Biesenthal


Readers

Aric Vyhmeister

Erik Biesenthal

John Hawkins

Tyler Anderson

Comments

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 "\ ".