Three amplifiers each having voltage gain 10, are connected in series. The resultant gain would be

Options

A. 10
B. 30
C. 1000
D. `10/3`

Answer

To find the resultant gain of three amplifiers connected in series, each having a voltage gain of 10, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Gain of Each Amplifier**:
Each amplifier has a voltage gain (Av) of 10. This means:
- For the first amplifier: \( Av_1 = 10 \)
- For the second amplifier: \( Av_2 = 10 \)
- For the third amplifier: \( Av_3 = 10 \)

2. **Understand the Series Connection**:
When amplifiers are connected in series, the total or resultant gain (Av_total) is the product of the individual gains. Therefore:
\[ Av_{total} = Av_1 \times Av_2 \times Av_3 \]

3. **Substitute the Values**:
Now, substitute the values of the gains into the equation:
\[ Av_{total} = 10 \times 10 \times 10 \]

4. **Calculate the Resultant Gain**:
Perform the multiplication:
\[ Av_{total} = 1000 \]

5. **Conclusion**:
The resultant gain of the three amplifiers connected in series is 1000.

### Final Answer:
The resultant gain would be **1000**.

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