Question

The armature winding and field winding resistance of a 220 V, 100 A, 1500 rpm dc series motor are $0.05\Omega$ each. The motor is operated under dynamic braking at twice the rated torque and at 1000 rpm. The value of braking resistance is______

• A. $5.1\Omega$
• B. $4\Omega$
• C. $1.3\Omega$
• D. $2.6\Omega$

Answer 1

The correct option is C $1.3\Omega$

$T_1=K_f{I}_{a1}^2$ $(\therefore \varphi \propto I_a)$

$T_2=K_f{I}_{a2}^2$

$I_{a2}=I_{a1}\sqrt{\frac{T_2}{T_1}}=100\times \sqrt{2}=141.4A$

$E_1=K_e{I}_{a1}{N}_1$

$E_2=K_e{I}_{a2}{N}_2$

$E_2=E_1\times \frac{N_2}{N_1}\times \frac{I_{a2}}{I_{a1}}$

$=[220-(100\times 0.1\left)\right]\times \frac{1000}{1500}\times \frac{141.4}{100}=197.96V$

$E_2=I_{e2}\times (R_B+0.1)$

$197.96=141.4(R_B+0.1)$

$\Rightarrow Breakingresistance{R}_B=1.3\Omega$