If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of `beta` will be :

Options

A. 7
B. 0.5
C. 0.875
D. 3.5

Answer

To find the value of beta (β), which is the current gain of a transistor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between emitter current (I_E), collector current (I_C), and base current (I_B)**:
\[ I_E = I_C + I_B \]
This means that the emitter current is the sum of the collector current and the base current.

2. **Define the changes in current**:
We are given:
- Change in emitter current: \(\Delta I_E = 4 \, \text{mA}\)
- Change in collector current: \(\Delta I_C = 3.5 \, \text{mA}\)

3. **Find the change in base current (\Delta I_B)**:
Using the relationship from step 1, we can express the change in base current as:
\[ \Delta I_E = \Delta I_C + \Delta I_B \]
Rearranging gives:
\[ \Delta I_B = \Delta I_E - \Delta I_C \]
Substituting the values:
\[ \Delta I_B = 4 \, \text{mA} - 3.5 \, \text{mA} = 0.5 \, \text{mA} \]

4. **Calculate beta (β)**:
Beta is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]
Substituting the values we found:
\[ \beta = \frac{3.5 \, \text{mA}}{0.5 \, \text{mA}} = 7 \]

5. **Conclusion**:
The value of beta (β) is 7.

### Final Answer:
\[ \beta = 7 \]