In a common base mode of a transition , the collector current is `5.488 mA` for an emitter currect of `5.60 mA` . The value of the base current amplification factor `(beta)` will be

Options

A. `49`
B. `50`
C. `51`
D. `48`

Explanation

To find the base current amplification factor (β) in a common base mode of a transistor, we can follow these steps:

### Step 1: Understand the relationship between the currents
In a transistor, the relationship between the emitter current (I_E), collector current (I_C), and base current (I_B) is given by:
\[ I_E = I_C + I_B \]

### Step 2: Rearrange the equation to find I_B
From the equation above, we can express the base current (I_B) as:
\[ I_B = I_E - I_C \]

### Step 3: Substitute the given values
We are given:
- Collector current, \( I_C = 5.488 \, \text{mA} \)
- Emitter current, \( I_E = 5.60 \, \text{mA} \)

Now, substituting these values into the equation for I_B:
\[ I_B = 5.60 \, \text{mA} - 5.488 \, \text{mA} \]
\[ I_B = 0.112 \, \text{mA} \]

### Step 4: Calculate the base current amplification factor (β)
The base current amplification factor (β) is defined as:
\[ \beta = \frac{I_C}{I_B} \]

Now substituting the values we have:
\[ \beta = \frac{5.488 \, \text{mA}}{0.112 \, \text{mA}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \beta = \frac{5.488}{0.112} \approx 49 \]

### Final Answer
Thus, the value of the base current amplification factor (β) is approximately **49**.

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