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) ${\varphi }_m=\frac{E_1}{4.44f{N}_1}$ $=\frac{V_1}{4.44f{N}_1}$ $=\frac{240}{4.44*50*150}$ $=7.21mWb$