Ideal Transformer Example

An idea transformer has a 150-turn primary and 750-turn secondary. The primary is connected to a 240-V, 50-Hz source. The secondary supplies a load of 4 A at a lagging power factor of 0.8. Find the turns-ratio, the current in the primary, the power supplied to the load, and the flux in the core.

Solution

(A) $\ {turns-ratio}={\frac {N_{1}}{N_{2}}}$ $\ ={\frac {150}{750}}$ $\ =0.2$

(B) Because $\ {I_{2}}=4A$, the current in the primary is...

$\ {I_{1}}={\frac {I_{2}}{turns-ratio}}$ $\ ={\frac {4}{0.2}}$ $\ =20A$

(C) $\ {V_{2}}={\frac {V_{1}}{turns-ratio}}$ $\ ={\frac {240}{0.2}}$ $\ =1200V$

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

$\ {P_{L}}=V_{2}I_{2}\cos(\theta )$ $\ =1200*4*0.8$ $\ =3840W$

(D) $\ {\phi _{m}}={\frac {E_{1}}{4.44fN_{1}}}$ $\ ={\frac {V_{1}}{4.44fN_{1}}}$ $\ ={\frac {240}{4.44*50*150}}$ $\ =7.21mWb$