The closed loop transfer function of a negative feedback system is 10 and feedback factor is 0.05. What will be the open loop gain?

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HPCL Engineer Instrumentation 11 Aug 2021 Official Paper
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  1. 6.66
  2. 20
  3. -20
  4. -6.66

Answer (Detailed Solution Below)

Option 2 : 20
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Solution

Concept

The open loop gain is given by G(s) 

The feedback factor is given by H(s)

Hence the closed loop transfer function is given by \(\frac{G(s)}{1+G(s)H(s)}\)

Calculation

Given \(\frac{G(s)}{1+G(s)H(s)}\) = 10

H(s) = 0.05

To claculate G(s) we have

\(\frac{G(s)}{1+G(s)0.05}\) = 10

G(s)= 10 + 0.5G(s)

0.5 G(s) = 10

G(s) = 20

Hence the open loop Gain is 20

Therefore the correct answer is option 2

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