An amplifier has a voltage gain of 100. The voltage gain in dB is

Options

A. 20 dB
B. 40 dB
C. 30 dB
D. 50 dB

Explanation

To find the voltage gain in decibels (dB) for an amplifier with a voltage gain (Av) of 100, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The voltage gain in decibels (dB) can be calculated using the formula:
\[ \text{Voltage Gain (dB)} = 20 \log_{10}(A_v) \]
where \( A_v \) is the voltage gain.

2. **Substitute the Given Value**: In this case, the voltage gain \( A_v \) is given as 100. Substitute this value into the formula:
\[ \text{Voltage Gain (dB)} = 20 \log_{10}(100) \]

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

4. **Multiply by 20**: Now, substitute the value of the logarithm back into the equation:
\[ \text{Voltage Gain (dB)} = 20 \times 2 \]

5. **Final Calculation**: Perform the multiplication:
\[ \text{Voltage Gain (dB)} = 40 \, \text{dB} \]

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