For a transistor amplifier the collector load resistance ` R_L = 2 k Omega ` and the input resistance ` R_i = 1 k Omega ` . If the current again is 50 , calculate voltage gain of the amplifier .

Options

A. 100
B. 25
C. 50
D. 75

Answer

To calculate the voltage gain of the transistor amplifier, we can follow these steps:

### Step 1: Identify the given values
- Collector load resistance, \( R_L = 2 \, k\Omega = 2 \times 10^3 \, \Omega \)
- Input resistance, \( R_i = 1 \, k\Omega = 1 \times 10^3 \, \Omega \)
- Current gain (beta), \( \beta = 50 \)

### Step 2: Understand the formula for voltage gain
The voltage gain \( A_V \) of a transistor amplifier can be calculated using the formula:
\[ A_V = \beta \times \text{Resistance Gain} \]
Where the resistance gain is defined as the ratio of the load resistance to the input resistance:
\[ \text{Resistance Gain} = \frac{R_L}{R_i} \]

### Step 3: Calculate the resistance gain
Substituting the values of \( R_L \) and \( R_i \):
\[ \text{Resistance Gain} = \frac{R_L}{R_i} = \frac{2 \times 10^3 \, \Omega}{1 \times 10^3 \, \Omega} = \frac{2}{1} = 2 \]

### Step 4: Calculate the voltage gain
Now, substituting the values of \( \beta \) and the resistance gain into the voltage gain formula:
\[ A_V = \beta \times \text{Resistance Gain} = 50 \times 2 = 100 \]

### Step 5: Conclusion
The voltage gain of the amplifier is:
\[ A_V = 100 \]