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) ${\varphi }_m=\frac{E_1}{4.44f{N}_1}$ $=\frac{V_1}{4.44f{N}_1}$ $=\frac{200}{4.44*60*275}$ $=2.73mWb$

Author

Kyle Lafferty