In a common-base configuration of a transistor `(Delta i)/(Delta i_(e)) = 0.98`, then current gain in common emitter configuration of transistor will be

Options

A. 49
B. 98
C. 4.9
D. 24.5

Answer

To find the current gain in the common emitter configuration of a transistor given the current gain in the common base configuration, we can follow these steps:

### Step 1: Understand the relationship between alpha and beta
In a transistor, the current gain in common base configuration is denoted as \( \alpha \) and is defined as:
\[ \alpha = \frac{\Delta I_C}{\Delta I_E} \]
where \( I_C \) is the collector current and \( I_E \) is the emitter current.

The current gain in common emitter configuration is denoted as \( \beta \) and is defined as:
\[ \beta = \frac{I_C}{I_B} \]
where \( I_B \) is the base current.

### Step 2: Use the relationship between alpha and beta
The relationship between \( \alpha \) and \( \beta \) is given by:
\[ \beta = \frac{\alpha}{1 - \alpha} \]

### Step 3: Substitute the given value of alpha
From the question, we know that:
\[ \alpha = 0.98 \]
Now we can substitute this value into the equation for \( \beta \):
\[ \beta = \frac{0.98}{1 - 0.98} \]

### Step 4: Calculate the denominator
Calculate \( 1 - 0.98 \):
\[ 1 - 0.98 = 0.02 \]

### Step 5: Substitute and calculate beta
Now substitute back into the equation for \( \beta \):
\[ \beta = \frac{0.98}{0.02} \]

### Step 6: Perform the division
Now perform the division:
\[ \beta = 49 \]

### Conclusion
Thus, the current gain in the common emitter configuration of the transistor is:
\[ \beta = 49 \]