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

Options

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

Answer

To find the voltage gain of the amplifier without feedback, we can use the formula for the voltage gain with negative feedback:

\[ A_v = \frac{A_{v0}}{1 + \beta A_{v0}} \]

Where:
- \( A_v \) is the voltage gain with feedback,
- \( A_{v0} \) is the voltage gain without feedback,
- \( \beta \) is the feedback factor.

Given:
- \( A_v = 10 \) (the voltage gain with feedback),
- \( \beta = 9\% = \frac{9}{100} = 0.09 \).

We need to find \( A_{v0} \).

### Step 1: Substitute the known values into the formula

We can substitute the known values into the formula:

\[ 10 = \frac{A_{v0}}{1 + 0.09 A_{v0}} \]

### Step 2: Cross-multiply to eliminate the fraction

Cross-multiplying gives us:

\[ 10(1 + 0.09 A_{v0}) = A_{v0} \]

### Step 3: Distribute the 10

Distributing the 10 on the left side:

\[ 10 + 0.9 A_{v0} = A_{v0} \]

### Step 4: Rearrange the equation

Rearranging the equation to isolate \( A_{v0} \):

\[ 10 = A_{v0} - 0.9 A_{v0} \]

This simplifies to:

\[ 10 = 0.1 A_{v0} \]

### Step 5: Solve for \( A_{v0} \)

Now, we can solve for \( A_{v0} \):

\[ A_{v0} = \frac{10}{0.1} = 100 \]

Thus, the voltage gain without feedback is:

\[ \boxed{100} \]

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