An amplifier has a voltage gain of 500 without any feedback.Now a negative feedback is applied and its gain is 9.8 .then the feedback ratio is ?

Explanation

To solve the problem of finding the feedback ratio \( B \) for the given amplifier, we can follow these steps:

### Step 1: Understand the given data
We have the following information:
- Voltage gain without feedback, \( A = 500 \)
- Voltage gain with negative feedback, \( A_F = 9.8 \)

### Step 2: Write the feedback gain formula
The formula for the feedback gain \( A_F \) when negative feedback is applied is given by:
\[ A_F = \frac{A}{1 + AB} \]
where \( A \) is the open-loop gain and \( B \) is the feedback ratio.

### Step 3: Substitute the known values into the formula
Substituting the known values into the feedback gain formula:
\[ 9.8 = \frac{500}{1 + 500B} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 9.8(1 + 500B) = 500 \]

### Step 5: Expand the equation
Expanding the left side:
\[ 9.8 + 4900B = 500 \]

### Step 6: Rearrange the equation to isolate \( B \)
Now, rearranging the equation to solve for \( B \):
\[ 4900B = 500 - 9.8 \]
\[ 4900B = 490.2 \]

### Step 7: Solve for \( B \)
Now, divide both sides by 4900 to find \( B \):
\[ B = \frac{490.2}{4900} \]
\[ B = 0.1 \]

### Final Result
Thus, the feedback ratio \( B \) is:
\[ B = 0.1 \]

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