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 of 100, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for voltage gain in dB**:
The voltage gain (Av) in decibels is given by the formula:
\[ A_v(dB) = 10 \log_{10}(A_v) \]

2. **Substitute the given voltage gain into the formula**:
Here, the voltage gain \( A_v \) is 100. So we substitute this value into the formula:
\[ A_v(dB) = 10 \log_{10}(100) \]

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

4. **Multiply by 10**:
Now, substitute \( \log_{10}(100) \) back into the equation:
\[ A_v(dB) = 10 \times 2 \]

5. **Final calculation**:
\[ A_v(dB) = 20 \]

Thus, the voltage gain in decibels is **20 dB**.

### Final Answer:
The voltage gain in dB is **20 dB**.