Question

A 300 V dc series motor having series resistance equal to 0.3 $\Omega$ draws 50 A while delivering its rated output at 2000 rpm. The resistance required to be added to obtain rated torque at 1500 rpm will be

• A. 1.425 $\Omega$
• B. 1.86 $\Omega$
• C. 1.50 $\Omega$
• D. 1.66 $\Omega$

Answer 1

The correct option is A 1.425 $\Omega$

$E=V-I_a{R}_a=300-50\times 0.3=285V$

$E_1=\frac{P\varphi Z\left(2000\right)}{60A}$

$E_2=\frac{P\varphi \left(1500\right)}{60}\times \frac{Z}{A}$

$\frac{E_1}{E_2}=\frac{2000}{1500}=\frac{4}{3}$

$E_2=\frac{3}{4}\times E_1=\frac{3}{4}\times 285=213.75V$

$E_2=V-I_a(R_a+R^{\prime })$

$213.75=300-50(0.3+R^{\prime })$

$50(0.3+R^{\prime })=86.25$

$0.3+R^{\prime }=1.725$

$R^{\prime }=1.425\Omega$