In the case of constant `alpha` and `beta` of a transistor

Options

A. (1) alpha=beta`
B. `(2)beta lt 1, alpha gt 1`
C. `(3)alpha beta = 1`
D. `(4)beta gt 1, alpha lt 1`

Answer

To solve the question regarding the relationship between alpha (α) and beta (β) in a transistor when both are constant, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Alpha (α) is defined as the ratio of the collector current (I_C) to the emitter current (I_E):
\[ \alpha = \frac{I_C}{I_E} \]
- Beta (β) is defined as the ratio of the collector current (I_C) to the base current (I_B):
\[ \beta = \frac{I_C}{I_B} \]

2. **Analyze the Relationship between I_E, I_C, and I_B**:
- In a transistor, the emitter current (I_E) is the sum of the collector current (I_C) and the base current (I_B):
\[ I_E = I_C + I_B \]
- Since I_E is always greater than I_C (because I_B is always positive), we can conclude that:
\[ I_E > I_C \implies \alpha < 1 \]

3. **Determine the Value of Beta (β)**:
- Since the collector current (I_C) is greater than the base current (I_B) in a transistor:
\[ I_C > I_B \implies \beta > 1 \]

4. **Summarize the Findings**:
- From the above analysis, we have established that:
- Alpha (α) is always less than 1: \( \alpha < 1 \)
- Beta (β) is always greater than 1: \( \beta > 1 \)

5. **Select the Correct Option**:
- Based on the findings, the correct option from the given choices is:
- Option 4: Beta is greater than 1, and Alpha is less than 1.

### Final Answer:
The correct answer is Option 4: Beta is greater than 1, and Alpha is less than 1.

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