The voltage gain of an amplifier stage is 100. The gain expressed dB is :

Options

A. 100
B. 20
C. 40
D. 10

Answer

To solve the problem of finding the voltage gain of an amplifier stage expressed in decibels (dB), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Gain in dB**:
The voltage gain (A) in decibels (dB) can be calculated using the formula:
\[ \text{Gain (dB)} = 10 \log_{10}(A) \]
where \( A \) is the voltage gain (not in dB).

2. **Substitute the Given Gain**:
From the problem, we know that the voltage gain \( A = 100 \). We will substitute this value into the formula:
\[ \text{Gain (dB)} = 10 \log_{10}(100) \]

3. **Calculate the Logarithm**:
We need to calculate \( \log_{10}(100) \). We can express 100 as \( 10^2 \):
\[ \log_{10}(100) = \log_{10}(10^2) = 2 \]

4. **Multiply by 10**:
Now we can substitute back into the gain formula:
\[ \text{Gain (dB)} = 10 \times 2 = 20 \text{ dB} \]

5. **Final Answer**:
Therefore, the voltage gain of the amplifier stage expressed in dB is:
\[ \text{Gain (dB)} = 20 \text{ dB} \]

### Summary:
The voltage gain of an amplifier stage of 100 is expressed as 20 dB.