For a CE- transistor amplifier , the audio signal voltage across the collector resistance of ` 2 k Omega ` is 2 V . Suppose the current amplifiaction factor of the transistor is 100 . Find the input signal voltage and base current , if the base resistance is `1 k Omega` .

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Calculate the Collector Current (Ic)
We know that the voltage across the collector resistance (Rc) is given as 2 V and the resistance (Rc) is 2 kΩ.

Using Ohm's Law:
\[ I_C = \frac{V_C}{R_C} \]

Substituting the values:
\[ I_C = \frac{2 \, \text{V}}{2000 \, \Omega} = 0.001 \, \text{A} = 1 \, \text{mA} \]

### Step 2: Calculate the Base Current (Ib)
The current amplification factor (β) is given as 100. The relationship between the collector current (Ic) and the base current (Ib) is:
\[ \beta = \frac{I_C}{I_B} \]

Rearranging the formula to find Ib:
\[ I_B = \frac{I_C}{\beta} \]

Substituting the values:
\[ I_B = \frac{1 \, \text{mA}}{100} = \frac{1 \times 10^{-3} \, \text{A}}{100} = 1 \times 10^{-5} \, \text{A} = 10 \, \mu\text{A} \]

### Step 3: Calculate the Input Signal Voltage (Vi)
The input voltage (Vi) can be calculated using Ohm's Law again, where the base resistance (Rb) is given as 1 kΩ.

Using the formula:
\[ V_I = I_B \times R_B \]

Substituting the values:
\[ V_I = 10 \times 10^{-6} \, \text{A} \times 1000 \, \Omega = 10 \, \text{mV} \]

### Summary of Results
- Input Signal Voltage (Vi) = 10 mV
- Base Current (Ib) = 10 µA