In a common base transistor circuit, `I_C` is the Output current and `I_E` is the input current. The current gain `alpha` is

Options

A. Greater than one
B. Less than one
C. Equal to one
D. None of these

Answer

To find the current gain \( \alpha \) in a common base transistor circuit, we can follow these steps:

### Step 1: Understand the relationship between the currents
In a common base configuration, the input current \( I_E \) (emitter current) is related to the output current \( I_C \) (collector current) and the base current \( I_B \) by the equation:
\[ I_E = I_C + I_B \]

### Step 2: Express \( I_C \) in terms of \( I_E \) and \( I_B \)
From the equation above, we can rearrange it to express \( I_C \):
\[ I_C = I_E - I_B \]

### Step 3: Define the current gain \( \alpha \)
The current gain \( \alpha \) in a common base transistor is defined as the ratio of the output current \( I_C \) to the input current \( I_E \):
\[ \alpha = \frac{I_C}{I_E} \]

### Step 4: Substitute \( I_C \) into the current gain formula
Now we can substitute the expression for \( I_C \) from Step 2 into the formula for \( \alpha \):
\[ \alpha = \frac{I_E - I_B}{I_E} \]

### Step 5: Simplify the expression
We can simplify the expression for \( \alpha \):
\[ \alpha = 1 - \frac{I_B}{I_E} \]

### Step 6: Analyze the value of \( \alpha \)
Since \( I_B \) (base current) is always a positive quantity, the term \( \frac{I_B}{I_E} \) will also be a positive quantity. Therefore, \( \alpha \) will always be less than 1:
\[ \alpha < 1 \]

### Conclusion
Thus, the current gain \( \alpha \) in a common base transistor circuit is less than 1.