For a transistor `(I_(C))/(I_(E))=0.96`, then current gain for common emitter configuration

Options

A. 12
B. 6
C. 48
D. 24

Explanation

To find the current gain (β) for a common emitter configuration of a transistor given that \(\frac{I_C}{I_E} = 0.96\), we can follow these steps:

### Step 1: Understand the relationship between the currents
In a transistor, we have the following relationship:
\[ I_E = I_C + I_B \]
where:
- \(I_E\) is the emitter current,
- \(I_C\) is the collector current,
- \(I_B\) is the base current.

### Step 2: Express \(I_E\) in terms of \(I_C\)
From the given ratio \(\frac{I_C}{I_E} = 0.96\), we can express \(I_E\) as:
\[ I_E = \frac{I_C}{0.96} \]

### Step 3: Substitute \(I_E\) into the current relationship
Substituting \(I_E\) into the equation \(I_E = I_C + I_B\):
\[ \frac{I_C}{0.96} = I_C + I_B \]

### Step 4: Rearrange the equation to find \(I_B\)
Rearranging gives:
\[ I_B = \frac{I_C}{0.96} - I_C \]
Factoring out \(I_C\):
\[ I_B = I_C \left(\frac{1}{0.96} - 1\right) \]
Calculating the term in the parentheses:
\[ \frac{1}{0.96} - 1 = \frac{1 - 0.96}{0.96} = \frac{0.04}{0.96} = \frac{1}{24} \]
Thus, we have:
\[ I_B = \frac{I_C}{24} \]

### Step 5: Calculate the current gain (β)
The current gain (β) for a common emitter configuration is defined as:
\[ \beta = \frac{I_C}{I_B} \]
Substituting the expression for \(I_B\):
\[ \beta = \frac{I_C}{\frac{I_C}{24}} = 24 \]

### Final Answer
The current gain (β) for the common emitter configuration is:
\[ \beta = 24 \]

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