The collector current for a transistor is `6.6mA`, and its current gains `alpha` is `0.95`. Determine `I_(B)` and `beta`

Options

A. `beta=19 , I_B=350 muA`
B. `beta=19 , I_B=220 muA`
C. `beta=30, I_B=330 muA`
D. `beta=30, I_B=220 muA`

Answer

To solve the problem, we need to determine the base current \( I_B \) and the current gain \( \beta \) of the transistor, given the collector current \( I_C \) and the current gain \( \alpha \).

### Step-by-Step Solution:

1. **Given Values:**
- Collector Current, \( I_C = 6.6 \, \text{mA} \)
- Current Gain, \( \alpha = 0.95 \)

2. **Relation Between \( \alpha \), \( I_C \), and \( I_E \):**
- The relationship between the collector current \( I_C \), emitter current \( I_E \), and \( \alpha \) is given by:
\[ \alpha = \frac{I_C}{I_E} \]
- Rearranging this gives:
\[ I_E = \frac{I_C}{\alpha} \]

3. **Calculate \( I_E \):**
- Substitute the values into the equation:
\[ I_E = \frac{6.6 \, \text{mA}}{0.95} = 6.947 \, \text{mA} \approx 6.95 \, \text{mA} \]

4. **Calculate Base Current \( I_B \):**
- The base current \( I_B \) can be found using the relationship:
\[ I_B = I_E - I_C \]
- Substitute the values:
\[ I_B = 6.95 \, \text{mA} - 6.6 \, \text{mA} = 0.35 \, \text{mA} \]
- Convert to microamperes:
\[ I_B = 0.35 \, \text{mA} = 350 \, \mu\text{A} \]

5. **Calculate Current Gain \( \beta \):**
- The current gain \( \beta \) is defined as:
\[ \beta = \frac{I_C}{I_B} \]
- Substitute the values:
\[ \beta = \frac{6.6 \, \text{mA}}{0.35 \, \text{mA}} = \frac{6.6}{0.35} \approx 18.857 \approx 19 \]

### Final Results:
- Base Current, \( I_B = 0.35 \, \text{mA} = 350 \, \mu\text{A} \)
- Current Gain, \( \beta = 19 \)