Question

A 4 - pole series motor has 944 wave connected armature conductors. At a certain load, the flux per pole is 34.6 mWb and the total mechanical power developed is 4 kW; total motor resistance is $3\Omega$. The line current taken by the motor with an applied voltage of 500 V is _______A.

• A. 8.53

Answer 1

The correct option is A 8.53
$E_a=\frac{\varphi NZ}{60}\left(\frac{P}{A}\right)$ $...\left(i\right)$

$E_a{I}_a=4\times {10}^3$ $...\left(ii\right)$

$I_a=\frac{V-E_a}{R_a}$ $...\left(iii\right)$
$\text{Armature current ,}{I}_a=\frac{500-E_a}{3}$

$\text{For series motor,}{I}_a=I_L...\left(iv\right)$

$\text{Substituting the value of}{I}_a\text{in equation (ii), we get}$

$E_a\times \left(\frac{500-E_a}{3}\right)=4\times {10}^3$

$E_a^2-500E_a+12\times {10}^3=0$

$E_a=\frac{500\pm \sqrt{25\times {10}^4-4.8\times {10}^4}}{2}$

$=474.72V$

$\text{Armature current,}{I}_a=\frac{500-474.72}{3}=8.427A$