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 volt, calculate the output ac signal.

To find the output AC signal when two amplifiers are connected in series, we can use the concept of voltage gain. Each amplifier increases the voltage of the input signal based on its gain. In this case, we have two amplifiers: the first with a voltage gain of 10 and the second with a voltage gain of 20. Let's break down the calculation step by step.

Understanding Voltage Gain

Voltage gain is defined as the ratio of the output voltage to the input voltage. It can be expressed mathematically as:

Voltage Gain (A) = Output Voltage (V_out) / Input Voltage (V_in)

When amplifiers are cascaded, the total voltage gain is the product of the individual gains of each amplifier.

Calculating Total Voltage Gain

For our scenario, we have:

• First amplifier gain (A1) = 10
• Second amplifier gain (A2) = 20

The total voltage gain (A_total) can be calculated as:

A_total = A1 × A2

Substituting the values:

A_total = 10 × 20 = 200

Finding the Output Voltage

Now that we have the total voltage gain, we can find the output voltage using the input signal. The input signal (V_in) is given as 0.01 volts. The output voltage (V_out) can be calculated using the formula:

V_out = A_total × V_in

Substituting the known values:

V_out = 200 × 0.01 = 2 volts

Final Result

Therefore, the output AC signal after passing through both amplifiers is 2 volts. This demonstrates how cascading amplifiers can significantly increase the voltage of a signal, making it useful in various applications such as audio systems, radio transmissions, and more.