Question

The correct relation for $\alpha, \beta$ for a transistor

• A. $\beta=\frac{1-\alpha}{\alpha}$
• B. $\beta=\frac{\alpha}{1-\alpha}$
• C. $\alpha=\frac{\beta-1}{\beta}$
• D. $\alpha\beta=1.$

Answer 1

The Correct Option is B

To determine the correct relation between the parameters $\alpha$ and $\beta$ in a transistor, we need to understand the basic concepts of transistor operation.

In a transistor, especially a bipolar junction transistor (BJT), two parameters are crucial:

• $\alpha$: The common base current gain, defined as the ratio of the collector current $(I_C)$ to the emitter current $(I_E)$, i.e., $\alpha = \frac{I_C}{I_E}$.
• $\beta$: The common emitter current gain, defined as the ratio of the collector current $(I_C)$ to the base current $(I_B)$, i.e., $\beta = \frac{I_C}{I_B}$.

The relationship between $\alpha$ and $\beta$ can be derived from the current relations in a transistor:

• The total emitter current $(I_E)$ is the sum of the collector current $(I_C)$ and the base current $(I_B)$: $$I_E = I_C + I_B$$.
• Using the definitions of $\alpha$ and $\beta$: $$\alpha = \frac{I_C}{I_E}$$ and $$\beta = \frac{I_C}{I_B}$$.

To find a relation between $\alpha$ and $\beta$, we substitute $I_B = I_E - I_C$ into the expression for $\beta$:

$$\beta = \frac{I_C}{I_E - I_C}$$

Substituting $\alpha = \frac{I_C}{I_E}$ into the above expression, we get:

$$\beta = \frac{\alpha I_E}{I_E - \alpha I_E} = \frac{\alpha}{1 - \alpha}$$

Therefore, the correct relation between $\alpha$ and $\beta$ is $\beta = \frac{\alpha}{1 - \alpha}$.

This corresponds to the correct option given in the question.