Input signal to a common emitter amplifier having a voltage gain of 1000 is given by `v_(1) = (0.004 V)` `sin(omega t + pi/2)`. The corresponding output signal is

Options

A. `(40V) sin` `(omegat + pi/2)`
B. `(0.0004V) cos` `(omegat + pi/2)`
C. `(4V) cos` `(omegat + pi/2)`
D. `(4V) sin` `(omegat + pi/2)`

Answer

To find the corresponding output signal of a common emitter amplifier given the input signal and voltage gain, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Input Signal**:
The input signal is given as:
\[ v_1 = 0.004 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) \]

2. **Determine the Voltage Gain**:
The voltage gain (A) of the amplifier is given as:
\[ A = 1000 \]

3. **Understand the Relationship Between Input and Output**:
The output voltage (\(v_{out}\)) can be calculated using the formula:
\[ v_{out} = A \cdot v_{in} \]
where \(v_{in}\) is the input voltage.

4. **Calculate the Output Voltage**:
Substitute the values of \(A\) and \(v_{in}\) into the formula:
\[ v_{out} = 1000 \cdot (0.004 \, \text{V} \, \sin(\omega t + \frac{\pi}{2})) \]
\[ v_{out} = 4 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) \]

5. **Determine the Phase of the Output Signal**:
The phase of the output signal remains the same as that of the input signal because a common emitter amplifier does not change the phase. Thus, the output signal can be expressed as:
\[ v_{out} = 4 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) \]

6. **Final Output Signal**:
The output signal can also be expressed in a different form by using the sine addition formula:
\[ v_{out} = 4 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) = 4 \, \text{V} \, \cos(\omega t) \]
However, in the context of the problem, we will keep it in the sine form:
\[ v_{out} = 4 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) \]

### Final Answer:
The corresponding output signal is:
\[ v_{out} = 4 \, \text{V} \, \sin(\omega t + \frac{\pi}{2}) \]