A transistor has a current gain of 30. If the collector resistance is `6kOmega`, input resistance is `1kOmega`, calculate its volage gain?

Options

A. 90
B. 180
C. 45
D. 360

Explanation

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

### Step 1: Identify the given values
- Current gain (β) = 30
- Collector resistance (R_output) = 6 kΩ = 6000 Ω
- Input resistance (R_input) = 1 kΩ = 1000 Ω

### Step 2: Write the formula for voltage gain
The voltage gain (A_v) can be calculated using the formula:
\[ A_v = \beta \times \left( \frac{R_{output}}{R_{input}} \right) \]
where:
- \( \beta \) is the current gain,
- \( R_{output} \) is the collector resistance,
- \( R_{input} \) is the input resistance.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A_v = 30 \times \left( \frac{6000}{1000} \right) \]

### Step 4: Calculate the resistance gain
Calculate the resistance gain:
\[ \frac{R_{output}}{R_{input}} = \frac{6000}{1000} = 6 \]

### Step 5: Calculate the voltage gain
Now substitute the resistance gain back into the voltage gain formula:
\[ A_v = 30 \times 6 = 180 \]

### Step 6: State the final answer
The voltage gain of the transistor is:
\[ A_v = 180 \]