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The separately excited $dc$ motor in the figure below has a rated armature current of $20$ $A$ 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. $0.7$
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