The transfer function of the system shown in the following figure is:...

The transfer function of the system shown in the following figure is:

 

A. G₁G₂ + 1
B. G₁ + G₂ + 1
C. G₁G₂ + G₁ + 1
D. G₁G₂ + G₂ + 1

Step 1: Identify the signals
Input = R(s)
After block G₁ = G₁R(s)

Step 2: First summing junction
Inputs:
- Output of G₁ = G₁R(s)
- Direct input = R(s)

Therefore,
X(s) = G₁R(s) + R(s) = (G₁ + 1)R(s)

Step 3: Pass through G₂
Output = G₂ × X(s) = G₂(G₁ + 1)R(s)

Step 4: Second summing junction
Inputs:
- Output of G₂ = G₂(G₁ + 1)R(s)
- Direct input = R(s)

Therefore,
C(s) = G₂(G₁ + 1)R(s) + R(s)

Step 5: Transfer function
C(s)/R(s) = G₂(G₁ + 1) + 1

Expanding:
= G₁G₂ + G₂ + 1

Final Answer: Option D → G₁G₂ + G₂ + 1