The current gain of a transistor in common emitter configuration is 80. If the emitter current be 8.1 mA , then the collector current will be

Options

A. 8.1 mA
B. 8.0 mA
C. 0.1 mA
D. 1.0 mA

Explanation

To solve the problem step by step, we will use the formulas related to the current gain of a transistor in a common emitter configuration.

### Step 1: Identify the given values
- Current gain (β) = 80
- Emitter current (IE) = 8.1 mA

### Step 2: Write the formulas
1. The current gain (β) is defined as:
\[ \beta = \frac{I_C}{I_B} \]
where \(I_C\) is the collector current and \(I_B\) is the base current.

2. The emitter current (IE) is given by:
\[ I_E = I_B + I_C \]

### Step 3: Express \(I_C\) in terms of \(I_B\)
From the current gain formula, we can express the collector current \(I_C\) as:
\[ I_C = \beta \cdot I_B = 80 \cdot I_B \]

### Step 4: Substitute \(I_C\) in the emitter current equation
Now, substitute \(I_C\) in the emitter current equation:
\[ I_E = I_B + I_C \]
Substituting \(I_C\):
\[ 8.1 \, \text{mA} = I_B + 80 \cdot I_B \]
This simplifies to:
\[ 8.1 \, \text{mA} = 81 \cdot I_B \]

### Step 5: Solve for \(I_B\)
Now, we can solve for \(I_B\):
\[ I_B = \frac{8.1 \, \text{mA}}{81} = 0.1 \, \text{mA} \]

### Step 6: Calculate \(I_C\)
Now that we have \(I_B\), we can find \(I_C\):
\[ I_C = 80 \cdot I_B = 80 \cdot 0.1 \, \text{mA} = 8 \, \text{mA} \]

### Final Answer
The collector current \(I_C\) is **8 mA**.

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