Question

In the feedback scheme shown in figure, the time-constant of the closed loop system will be

• A. $A\beta \tau$
• B. $(1+A\beta \tau )$
• C. $\tau$
• D. $\frac{\tau }{(1+A\beta )}$

Answer 1

The correct option is D $\frac{\tau }{(1+A\beta )}$

$T\left(s\right)=\frac{C\left(s\right)}{R\left(s\right)}=\frac{A}{1+s\tau +A\beta }$
$=\frac{\frac{A}{1+A\beta }}{1+\frac{s\tau }{1+A\beta }}$ ....(i)
or $T\left(s\right)=\frac{\alpha }{1+{\tau }^{\prime }\beta }$. ....(ii)
Comparing equation (i) and (ii) we get
Thus, time constant ${\tau }^{\prime }=\frac{\tau }{1+A\beta }$