An amplifier has a voltage gain `A_(v)= 1000`. The voltage gain in `dB` is:

Options

A. 30 dB
B. 60 dB
C. 3 dB
D. 20 dB

Explanation

To find the voltage gain in decibels (dB) for an amplifier with a voltage gain \( A_v = 1000 \), we can use the formula for converting voltage gain to decibels:

\[ A_v' = 10 \log_{10}(A_v) \]

### Step-by-Step Solution:

1. **Identify the given voltage gain**:
\[ A_v = 1000 \]

2. **Substitute the value of \( A_v \) into the formula**:
\[ A_v' = 10 \log_{10}(1000) \]

3. **Calculate \( \log_{10}(1000) \)**:
- We know that \( 1000 = 10^3 \).
- Therefore, \( \log_{10}(1000) = \log_{10}(10^3) = 3 \).

4. **Substitute back into the equation**:
\[ A_v' = 10 \times 3 \]

5. **Calculate the final result**:
\[ A_v' = 30 \]

Thus, the voltage gain in decibels is:
\[ \boxed{30 \text{ dB}} \]