Question

What is amplification? In a common emitter amplifier, collector current is increased by 1 milliampere by increasing base current by 5 $\mu$ ampere. Calculate current gain $\alpha$ and $\beta$.

Hint:

The current gain \( \beta \) is the ratio of the change in collector current to the change in base current, while \( \alpha \) is the ratio of the change in collector current to the total current.

Answer 1

Step 1: Definition of Amplification.
Amplification refers to the process of increasing the amplitude of a signal. In the context of electronic circuits, it is the process by which the amplitude of an electrical signal (voltage or current) is increased without altering its other characteristics, such as frequency.
Step 2: Given Data.
- Increase in collector current, \( \Delta I_C = 1 \, \text{mA} = 10^{-3} \, \text{A} \),
- Increase in base current, \( \Delta I_B = 5 \, \mu\text{A} = 5 \times 10^{-6} \, \text{A} \).
Step 3: Current Gain \( \alpha \) and \( \beta \).
In a common emitter amplifier, the current gain \( \beta \) and \( \alpha \) are related as: \[ \beta = \frac{\Delta I_C}{\Delta I_B} \] Substitute the given values: \[ \beta = \frac{1 \times 10^{-3}}{5 \times 10^{-6}} = 200 \] The current gain \( \alpha \) is related to \( \beta \) by the formula: \[ \alpha = \frac{\beta}{\beta + 1} \] Substitute the value of \( \beta \): \[ \alpha = \frac{200}{200 + 1} = \frac{200}{201} \approx 0.995 \]
Final Answer:
The current gain is \( \boxed{\alpha = 0.995} \) and \( \boxed{\beta = 200} \).