The separately excited $dc$ motor in the figure below has a rated armature current of $20A$ and a rated armature voltage of $150$ $V$. An ideal chopper switching at $5\:kHz$ is used to control the armature voltage. If $L_a$= $0.1$ $mH$, $R_a= 1\Omega$, neglecting armature reaction, the duty ratio of the chopper to obtain $50\%$ of the rated torque at the rated speed and the rated field current is
1. $0.4$
2. $0.5$
3. $0.6$
4. $0.7$