The voltage gain of an amplifier with $9\%$ negative feedback is $10$. The voltage gain without feedback will

Question

The voltage gain of an amplifier with $9\%$ negative feedback is $10$. The voltage gain without feedback will be:

Accepted Answer

1. **Identify the Given Data:**
   * Voltage gain with feedback, $A_f = 10$
   * Feedback fraction, $\beta = 9\% = 0.09$
2. **State the Formula:** The formula for the voltage gain of an amplifier with negative feedback is given by:
   $$A_f = \frac{A}{1 + A\beta}$$
   where $A$ is the voltage gain without feedback.
3. **Perform the Calculation:**
   Substitute the given values into the formula:
   $$10 = \frac{A}{1 + A(0.09)}$$
   $$10(1 + 0.09A) = A$$
   $$10 + 0.9A = A$$
   $$A - 0.9A = 10$$
   $$0.1A = 10$$
   $$A = \frac{10}{0.1} = 100$$
4. **Conclusion:** The voltage gain without feedback is $100$.

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