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

Options

A. 1.25
B. 100
C. 90
D. 10

Answer

To find the voltage gain of an amplifier without feedback, we can use the relationship between the voltage gain with feedback (AVF), the actual voltage gain (AV), and the feedback factor (β).

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The voltage gain with 9% negative feedback (AVF) is given as 10.
- The feedback factor (β) is 9%, which can be expressed as a decimal: β = 9/100 = 0.09.

2. **Use the Feedback Formula**:
The relationship between the voltage gain with feedback (AVF), the actual voltage gain (AV), and the feedback factor (β) is given by the formula:
\[ AVF = \frac{AV}{1 + β \cdot AV} \]

3. **Substitute the Known Values**:
We know that AVF = 10 and β = 0.09. Substitute these values into the formula:
\[ 10 = \frac{AV}{1 + 0.09 \cdot AV} \]

4. **Cross Multiply to Eliminate the Fraction**:
Cross multiplying gives us:
\[ 10(1 + 0.09 \cdot AV) = AV \]
Expanding this, we get:
\[ 10 + 0.9 \cdot AV = AV \]

5. **Rearrange the Equation**:
Rearranging the equation to isolate AV:
\[ AV - 0.9 \cdot AV = 10 \]
This simplifies to:
\[ 0.1 \cdot AV = 10 \]

6. **Solve for AV**:
Dividing both sides by 0.1 gives:
\[ AV = \frac{10}{0.1} = 100 \]

7. **Conclusion**:
The actual voltage gain without feedback (AV) is 100.

### Final Answer:
The voltage gain without feedback is **100**.