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 find 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 voltage gain in dB**:
The formula to convert voltage gain (A) to decibels (dB) is given by:
\[ \text{Gain (dB)} = 20 \log_{10}(A) \]

2. **Identify the voltage gain**:
In this problem, the voltage gain \( A \) is given as 100.

3. **Substitute the value of A into the formula**:
We substitute \( A = 100 \) into the formula:
\[ \text{Gain (dB)} = 20 \log_{10}(100) \]

4. **Calculate \( \log_{10}(100) \)**:
We know that \( 100 \) can be expressed as \( 10^2 \). Therefore:
\[ \log_{10}(100) = \log_{10}(10^2) = 2 \]

5. **Substitute back into the formula**:
Now we substitute \( \log_{10}(100) = 2 \) back into the equation:
\[ \text{Gain (dB)} = 20 \times 2 \]

6. **Calculate the final result**:
Multiplying gives:
\[ \text{Gain (dB)} = 40 \]

Thus, the gain expressed in dB is **40 dB**.