Question

In the case of constant ' \(\alpha\) ' and ' \(\beta\) ' of a transistor ( \(\alpha\) and \(\beta\) are current ratios)

• A. \(\beta<1, \alpha>1\)
• B. \(\beta>1, \alpha<1\)
• C. \(\alpha = \beta\)
• D. \(\alpha = \beta^2\)

Hint:

\(\alpha\) is slightly less than 1, \(\beta\) is large.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Transistor current gains describe how much current flows through the collector compared to either the emitter or the base.
Because the emitter current is the source for both base and collector current, \(I_E>I_C\) and \(I_C \gg I_B\).
Step 2: Key Formula or Approach:
Current relation: \(I_E = I_C + I_B\).
Current gain in common base: \(\alpha = \frac{I_C}{I_E}\).
Current gain in common emitter: \(\beta = \frac{I_C}{I_B}\).
Step 3: Detailed Explanation:
Since \(I_C\) is always a bit smaller than \(I_E\) (as some carriers are lost to the base), the ratio \(\alpha = I_C / I_E\) must be less than 1 (\(\alpha<1\)).
In a properly functioning transistor, the base current \(I_B\) is very small compared to the collector current \(I_C\).
Therefore, the ratio \(\beta = I_C / I_B\) must be much greater than 1 (\(\beta>1\)).
This explains why transistors are used for current amplification in common emitter mode.
Step 4: Final Answer:
The correct condition is \(\beta>1\) and \(\alpha<1\).