Choose the corrector relation between the transistor parameters `alpha` and `beta`.

Options

A. `beta=(alpha+1)/(alpha)`
B. `beta=(alpha-1)/(alpha)`
C. `beta=(alpha)/(1- alpha)`
D. `beta=(alpha)/(1+ alpha)`

Answer

To find the correct relation between the transistor parameters α (alpha) and β (beta), we can follow these steps:

### Step 1: Understand the Definitions
- **α (alpha)**: It is the common-base current gain defined as the ratio of the collector current (Ic) to the emitter current (Ie). Mathematically, it is given by:
\[ \alpha = \frac{I_c}{I_e} \]

- **β (beta)**: It is the common-emitter current gain defined as the ratio of the collector current (Ic) to the base current (Ib). Mathematically, it is given by:
\[ \beta = \frac{I_c}{I_b} \]

### Step 2: Relate the Currents
From the definitions, we know that:
- The emitter current (Ie) can be expressed in terms of the collector current (Ic) and the base current (Ib):
\[ I_e = I_c + I_b \]

### Step 3: Express Ib in terms of Ie and Ic
From the equation above, we can rearrange it to express Ib:
\[ I_b = I_e - I_c \]

### Step 4: Substitute Ib in the Beta Equation
Now we can substitute Ib in the beta equation:
\[ \beta = \frac{I_c}{I_b} = \frac{I_c}{I_e - I_c} \]

### Step 5: Substitute Ic in terms of Alpha
Using the definition of α, we can express Ic in terms of Ie:
\[ I_c = \alpha I_e \]
Substituting this into the beta equation gives:
\[ \beta = \frac{\alpha I_e}{I_e - \alpha I_e} \]

### Step 6: Simplify the Expression
Now we can simplify the expression:
\[ \beta = \frac{\alpha I_e}{I_e(1 - \alpha)} = \frac{\alpha}{1 - \alpha} \]

### Conclusion
Thus, the relation between α and β is:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

### Final Answer
The correct relation between the transistor parameters α and β is:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

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