Question

A three phase, 440 V, 50 Hz supply is feeding a 440 V, 15 kW, 1500 rpm separately excited dc motor with ripple free continuous current through a thyristor bridge. Neglecting all the losses, the power factor of the ac mains at half the rated speed is

• A. 0.353
• B. 0.955
• C. 0.372
• D. 0.90

Answer 1

The correct option is A 0.353

Here, it is mentioned in the given data that there is no losses.

$V_0=\frac{3V_{mL}}{\pi }\cos \alpha =E$

Since, back emf $E\propto N$

$\frac{E_1}{E_2}=\frac{N_1}{N_2}$

$E_1=2E_2(\therefore N_2=\frac{1}{2}{N}_1)$

So, $E_2=\frac{E_1}{2}=\frac{V_0}{2}=220V$

$\frac{3\times \sqrt{2}\times 440}{\pi }\cos \alpha =220$

$\cos \alpha =\frac{200\times \pi }{3\times \sqrt{2}\times 440}=0.3702$

Input power factor of the supply

$=\frac{3}{\pi }\cos \alpha =\frac{3}{\pi }\times 0.3702=0.353$