Question:
For the feedback system shown, the transfer function \(\dfrac{E(s)}{R(s)}\) is:
For the feedback system shown, the transfer function \(\dfrac{E(s)}{R(s)}\) is:
Show Hint
Always use \(C = GE\) in feedback loops to derive relationships. The error signal ratio is always \(1/(1+GH)\).
Updated On: Dec 29, 2025
- \(\dfrac{G}{1+GH}\)
- \(\dfrac{GH}{1+GH}\)
- \(\dfrac{1}{1+GH}\)
- \(\dfrac{1}{1+G}\)
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The Correct Option is C
Solution and Explanation
Step 1: Write the standard feedback equation.
For unity summing junction:
\[
E(s) = R(s) - H(s)C(s)
\]
Step 2: Substitute forward path output.
Since \(C(s) = G(s)E(s)\):
\[
E(s) = R(s) - H G E(s)
\]
Step 3: Solve for \(\dfrac{E(s)}{R(s)}\).
\[
E(s)(1 + GH) = R(s)
\]
\[
\frac{E(s)}{R(s)} = \frac{1}{1 + GH}
\]
Step 4: Conclusion.
The correct option is (C).
Final Answer: \(\boxed{\dfrac{1}{1+GH}}\)
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