Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of 10 and the second has a voltage gain of 20 . If the input signal is 0.01 V , calcualte the output AC signal .

Explanation

To calculate the output AC signal from two cascaded amplifiers, we can follow these steps:

### Step 1: Understand the Voltage Gain
The voltage gain (A) of an amplifier is defined as the ratio of the output voltage (V_out) to the input voltage (V_in). For cascaded amplifiers, the total voltage gain is the product of the individual gains.

### Step 2: Identify the Gains
- The voltage gain of the first amplifier (A1) = 10
- The voltage gain of the second amplifier (A2) = 20

### Step 3: Calculate the Total Voltage Gain
The total voltage gain (A_total) of the cascaded amplifiers can be calculated using the formula:
\[ A_{\text{total}} = A_1 \times A_2 \]
Substituting the values:
\[ A_{\text{total}} = 10 \times 20 = 200 \]

### Step 4: Calculate the Output Voltage
Now, we can calculate the output voltage (V_out) using the formula:
\[ V_{\text{out}} = A_{\text{total}} \times V_{\text{in}} \]
Where:
- \( V_{\text{in}} = 0.01 \, V \)

Substituting the values:
\[ V_{\text{out}} = 200 \times 0.01 = 2 \, V \]

### Conclusion
The output AC signal from the cascaded amplifiers is **2 V**.

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