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 solve the problem of finding 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. **Understand the Gain of Each Amplifier**:
Each amplifier has a voltage gain (A) of 10. This means that if an input voltage (V_in) is applied to the amplifier, the output voltage (V_out) will be 10 times the input voltage.

2. **Identify the Configuration**:
The amplifiers are connected in series. In a series configuration, the output of one amplifier becomes the input to the next amplifier.

3. **Calculate the Resultant Gain**:
When amplifiers are connected in series, the total or resultant gain (G_total) is the product of the individual gains.
\[ G_{\text{total}} = G_1 \times G_2 \times G_3 \]
Here, \(G_1 = 10\), \(G_2 = 10\), and \(G_3 = 10\).

4. **Perform the Multiplication**:
Substitute the values into the equation:
\[ G_{\text{total}} = 10 \times 10 \times 10 \]
\[ G_{\text{total}} = 1000 \]

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

### Final Answer:
The resultant gain of the three amplifiers connected in series is **1000**.

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