The amplifiers `X, Y` and `Z` are connected in series. If the voltage gains of `X, Y` and `Z` are `10, 20` and `30`, respectively and the input signal is `1mV` peak value, then what is the output signal voltage (peak value)
(i) if dc supply voltage is 10V ?
(ii) if dc supply voltage is 5V?

Options

A. 4V
B. 5 V
C. 6 V
D. 7 V

Answer

To solve the problem, we will calculate the output signal voltage (peak value) for both conditions: when the DC supply voltage is 10V and when it is 5V.

### Step-by-Step Solution:

1. **Identify the Voltage Gains**:
- The voltage gain of amplifier X (A_X) = 10
- The voltage gain of amplifier Y (A_Y) = 20
- The voltage gain of amplifier Z (A_Z) = 30

2. **Calculate the Total Voltage Gain**:
- The total voltage gain (A_total) of the series connection of amplifiers is the product of the individual gains:
\[ A_{total} = A_X \times A_Y \times A_Z = 10 \times 20 \times 30 \]

3. **Calculate A_total**:
- Performing the multiplication:
\[ A_{total} = 10 \times 20 = 200 \]
\[ A_{total} = 200 \times 30 = 6000 \]

4. **Input Signal**:
- The input signal voltage (V_in) = 1 mV = 0.001 V

5. **Calculate the Output Voltage**:
- The output voltage (V_out) can be calculated using the formula:
\[ V_{out} = A_{total} \times V_{in} \]
- Substituting the values:
\[ V_{out} = 6000 \times 0.001 = 6 \text{ V} \]

6. **Consider the DC Supply Voltage**:
- (i) If the DC supply voltage (V_CC) is 10V:
- The output voltage cannot exceed the supply voltage. Since 6V < 10V, the output voltage remains 6V.
- (ii) If the DC supply voltage (V_CC) is 5V:
- The output voltage cannot exceed the supply voltage. Since 6V > 5V, the output voltage will be limited to 5V.

### Final Output:
- (i) If DC supply voltage is 10V, the output signal voltage (peak value) = **6V**.
- (ii) If DC supply voltage is 5V, the output signal voltage (peak value) = **5V**.