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 , calculate the output AC signal .

Options

A. 4V
B. 1V
C. 2V
D. 6 V

Answer

To solve the problem of finding the output AC signal when two amplifiers are connected in series, we can follow these steps:

### Step 1: Understand the Given Information
We have two amplifiers connected in series:
- The first amplifier has a voltage gain (A1) of 10.
- The second amplifier has a voltage gain (A2) of 20.
- The input signal (Vin) is 0.01 V.

### Step 2: Calculate the Total Voltage Gain
The total voltage gain (A) of the cascaded amplifiers is the product of the individual gains:
\[ A = A1 \times A2 \]
Substituting the values:
\[ A = 10 \times 20 \]
Calculating this gives:
\[ A = 200 \]

### Step 3: Use the Voltage Gain Formula
The voltage gain can also be expressed in terms of the input and output voltages:
\[ A = \frac{V_{out}}{V_{in}} \]
We can rearrange this formula to find the output voltage (Vout):
\[ V_{out} = A \times V_{in} \]

### Step 4: Substitute the Values
Now substitute the values of A and Vin into the equation:
\[ V_{out} = 200 \times 0.01 \]
Calculating this gives:
\[ V_{out} = 2 \, \text{V} \]

### Step 5: Conclusion
The output AC signal voltage (Vout) is 2 V.

### Final Answer
The output AC signal is 2 V.

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