The current gain for a common emitter amplifier is 69. If the emitter current is 7 mA, the base current is

Options

A. 0.1 mA
B. 1 mA
C. 0.2 mA
D. 2 mA

Answer

To find the base current (Ib) for a common emitter amplifier given the current gain (β) and the emitter current (Ie), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Current gain (β) = 69
- Emitter current (Ie) = 7 mA = 7 × 10^-3 A

2. **Understand the Relationship Between Currents:**
- The relationship between emitter current (Ie), base current (Ib), and collector current (Ic) is given by:
\[ Ic = β \cdot Ib \]
- The emitter current is related to the collector and base currents as:
\[ Ie = Ic + Ib \]

3. **Express Collector Current in Terms of Base Current:**
- From the first equation, we can express Ic as:
\[ Ic = β \cdot Ib \]

4. **Substitute Ic in the Emitter Current Equation:**
- Substitute Ic in the equation for Ie:
\[ Ie = β \cdot Ib + Ib \]
- This can be simplified to:
\[ Ie = Ib (β + 1) \]

5. **Rearranging to Find Base Current (Ib):**
- Rearranging the equation gives:
\[ Ib = \frac{Ie}{β + 1} \]

6. **Substituting the Known Values:**
- Substitute the known values into the equation:
\[ Ib = \frac{7 \times 10^{-3}}{69 + 1} \]
- This simplifies to:
\[ Ib = \frac{7 \times 10^{-3}}{70} \]

7. **Calculate the Base Current (Ib):**
- Performing the division:
\[ Ib = 0.1 \times 10^{-3} \text{ A} = 0.1 \text{ mA} \]

### Final Answer:
The base current (Ib) is **0.1 mA**.