Question

Consider the following block diagram.

Overall gain C(s)/R(s) of the above system is

• A. 1.316
• B. -1.316
• C. 1.456
• D. -1.456

Answer 1

The correct option is B -1.316

Forword paths:

$F_1=4\times 20=80$

$F_2=4\times 3\times 2=24$

Non-touching loops are zero for both forward paths.

Individual loops:

$L_1=-4\times 3\times 2=-24$

$L_2=20\times 4=80$

$L_3=3\times 2\times 4=24$

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{80+24}{1-(-24+80+24)}$

$=\frac{104}{1-80}=\frac{104}{-79}=-1.316$