The current gain of 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 emitter current (IE) to 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 Current Gain (β)**:
The current gain (β) in a common emitter configuration is defined as the ratio of the collector current (IC) to the base current (IB):
\[ \beta = \frac{I_C}{I_B} \]
Given that β = 40, we can express this as:
\[ I_C = 40 I_B \quad \text{(Equation 1)} \]

2. **Relate Emitter Current (IE) to Collector and Base Currents**:
The relationship between the emitter current (IE), collector current (IC), and base current (IB) is given by:
\[ I_E = I_C + I_B \]

3. **Substitute IC from Equation 1 into the Emitter Current Equation**:
Substitute \(I_C\) from Equation 1 into the emitter current equation:
\[ I_E = (40 I_B) + I_B \]
Simplifying this gives:
\[ I_E = 41 I_B \quad \text{(Equation 2)} \]

4. **Find the Ratio of Emitter Current to Base Current**:
To find the ratio of emitter current (IE) to base current (IB), we can write:
\[ \frac{I_E}{I_B} = 41 \]

Thus, the ratio of emitter current to base current is **41**.

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