For a common emitter amplifier, the audio frequency voltage across the collector resistance `2kOmega` is 2V. If the current amplication factor of the transistor is 200, and the base resistance is `1.5 kOmega`, the input signal voltage and base current are

Options

A. 0.0075 V and `5 muA`
B. 0.1 V and `1 muA`
C. 0.15 V and `10 muA`
D. 0.015 V and 1A

Explanation

To solve the problem step by step, we will find the input signal voltage (Vi) and the base current (Ib) for the common emitter amplifier.

### Step 1: Calculate the Output Current (Ic)
The output voltage (Vo) across the collector resistance (Rc) is given as 2V, and the collector resistance (Rc) is 2 kΩ. We can calculate the collector current (Ic) using Ohm's Law:

\[ Ic = \frac{Vo}{Rc} \]

Substituting the values:

\[ Ic = \frac{2V}{2kΩ} = \frac{2}{2000} = 0.001 A = 1 mA \]

### Step 2: Calculate the Input Voltage (Vi)
The voltage gain (Av) of the amplifier can be expressed as:

\[ Av = \frac{Vo}{Vi} = \beta \cdot \frac{Rc}{Rb} \]

Where:
- \( \beta \) is the current amplification factor (200),
- \( Rc \) is the collector resistance (2 kΩ),
- \( Rb \) is the base resistance (1.5 kΩ).

Rearranging the equation to find Vi:

\[ Vi = \frac{Vo \cdot Rb}{\beta \cdot Rc} \]

Substituting the known values:

\[ Vi = \frac{2V \cdot 1.5kΩ}{200 \cdot 2kΩ} \]

Calculating:

\[ Vi = \frac{2 \cdot 1500}{200 \cdot 2000} = \frac{3000}{400000} = 0.0075 V \]

### Step 3: Calculate the Base Current (Ib)
Using the relationship between collector current (Ic) and base current (Ib):

\[ \beta = \frac{Ic}{Ib} \implies Ib = \frac{Ic}{\beta} \]

Substituting the values:

\[ Ib = \frac{1mA}{200} = \frac{0.001 A}{200} = 5 \times 10^{-6} A = 5 \mu A \]

### Final Results
- Input Signal Voltage (Vi) = 0.0075 V
- Base Current (Ib) = 5 μA