Question

A single phase induction motor has stator windings in space quadrature and is supplied with a single phase voltage of 200 V at 50 Hz. The stand still impedance of the main winding is $(5.2+j10.1)\Omega$ and that of auxiliary winding is $(19.7+j14.2)\Omega .$ The value of capacitance to be inserted in the auxiliary winding for maximum starting torque is____ $\mu F.$

• A. 130.5

Answer 1

The correct option is A 130.5

$Z_{m1}=(5.2+j10.1)\Omega$

$Z_a=(19.7+j14.2)\Omega$

$\text{For maximum starting torque}$

${\varphi }_a+{\varphi }_{m1}={90}^{\circ }...\left(i\right)$

${\varphi }_{m1}={62.76}^{\circ }$

$\text{So using equation (i)}$

$\varphi ={27.24}^{\circ }$

${\tan }^{-1}\frac{X_C-14.2}{19.7}={27.24}^{\circ }$

$\Rightarrow X_C=24.34\Omega$

$\omega C=0.0410$

$C=\frac{0.041}{(2\times \pi \times 50)}=130.7\mu F$