GATE ECE 2015 Set 2 | Question: 20

Question

For the signal flow graph shown in the figure, the value of $\dfrac{C(s)}{R(s)}$ is

 

• A. $\dfrac{G_{1}G_{2}G_{3}G_{4}}{1 – G_{1}G_{2}H_{1} – G_{3}G_{4}H_{2} – G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}} \\$
• B. $\dfrac{G_{1}G_{2}G_{3}G_{4}}{1  +  G_{1}G_{2}H_{1}  +  G_{3}G_{4}H_{2}  +  G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}} \\$
• C. $\dfrac{1}{1 + G_{1}G_{2}H_{1} + G_{3}G_{4}H_{2} + G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}} \\$
• D. $\dfrac{1}{1 – G_{1}G_{2}H_{1} – G_{3}G_{4}H_{2} – G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$