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The open-loop transfer function of a dc motor is given as $\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.$ When connected  in feedback as shown below, the approximate value of $K_{a}$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

  1. $1$
  2. $5$
  3. $10$
  4. $100$ 
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