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.

Solution

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

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

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

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

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

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

(D) $\ {\phi _{m}}={\frac {E_{1}}{4.44fN_{1}}}$ $\ ={\frac {V_{1}}{4.44fN_{1}}}$ $\ ={\frac {200}{4.44*60*275}}$ $\ =2.73mWb$