Question

For the system shown in figure the transfer function $\frac{C\left(s\right)}{R\left(s\right)}$ is equal to :

• A. $\frac{10}{s^2+s+10}$
• B. $\frac{10}{s^2+11s+10}$
• C. $\frac{10}{s^2+9s+10}$
• D. $\frac{10}{s^2+2s+10}$

Answer 1

The correct option is B $\frac{10}{s^2+11s+10}$

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{\frac{\frac{10}{s(s+1)}}{1+\frac{10}{s(s+1)}\times s}}{1+\frac{\frac{10}{s(s+1)}}{1+\frac{10}{s(s+1)}\times s}\times 1}$
$\frac{C\left(s\right)}{R\left(s\right)}=\frac{\frac{10}{s(s+1)+10s}}{1+\frac{10}{s(s+1)+10s}}=\frac{10}{s^2+s+10s+10}$
$\frac{C\left(s\right)}{R\left(s\right)}=\frac{10}{s^2+11s+10}$