The current gain of a transistor in a common emitter circuit is 40.The ratio of emitter current to base current is

Options

A. 40
B. 41
C. 42
D. 43

Answer

To solve the problem, we need to find the ratio of the emitter current (IE) to the base current (IB) given that the current gain (β) of the transistor in a common emitter configuration is 40.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The current gain (β) in a common emitter configuration is defined as the ratio of the change in collector current (IC) to the change in base current (IB):
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]
- Given that β = 40, we can write:
\[ \Delta I_C = 40 \Delta I_B \]

2. **Use the Relationship Between Currents**:
- The relationship between the emitter current (IE), collector current (IC), and base current (IB) is given by:
\[ I_E = I_C + I_B \]
- Therefore, we can express IE in terms of IB:
\[ I_E = \Delta I_C + \Delta I_B \]

3. **Substitute for IC**:
- From our earlier expression for IC, substitute \(\Delta I_C\):
\[ I_E = (40 \Delta I_B) + \Delta I_B \]
- This simplifies to:
\[ I_E = 41 \Delta I_B \]

4. **Find the Ratio of Emitter Current to Base Current**:
- The ratio of emitter current (IE) to base current (IB) is:
\[ \frac{I_E}{I_B} = \frac{41 \Delta I_B}{\Delta I_B} \]
- This simplifies to:
\[ \frac{I_E}{I_B} = 41 \]

5. **Conclusion**:
- The ratio of emitter current to base current is 41.

### Final Answer:
The ratio of emitter current to base current is **41**.

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