The current gain for common emitter amplifier is 69. If the emitter current is `7.0 mA`, find (i) base current and (ii) collector current.

Options

A. 4 mA
B. 4.4 mA
C. 3.8 mA
D. zero

Answer

To solve the problem step by step, we will use the relationships between the emitter current (Ie), base current (Ib), and collector current (Ic) in a common emitter amplifier.

### Given:
- Current gain (β) = 69
- Emitter current (Ie) = 7.0 mA

### Step 1: Understand the relationships
In a common emitter configuration, the following relationships hold:
1. \( \beta = \frac{I_c}{I_b} \) (Equation 1)
2. \( I_e = I_c + I_b \) (Equation 2)

### Step 2: Express Ic in terms of Ib
From Equation 1, we can express the collector current (Ic) in terms of base current (Ib):
\[ I_c = \beta \cdot I_b \]
Substituting this into Equation 2 gives:
\[ I_e = \beta \cdot I_b + I_b \]
This simplifies to:
\[ I_e = (\beta + 1) \cdot I_b \]

### Step 3: Substitute the known values
Now we can substitute the known values into the equation:
\[ 7.0 \, \text{mA} = (69 + 1) \cdot I_b \]
\[ 7.0 \, \text{mA} = 70 \cdot I_b \]

### Step 4: Solve for Ib (base current)
Now, we can solve for Ib:
\[ I_b = \frac{7.0 \, \text{mA}}{70} \]
\[ I_b = 0.1 \, \text{mA} \]

### Step 5: Calculate Ic (collector current)
Now that we have the base current, we can find the collector current using Equation 1:
\[ I_c = \beta \cdot I_b \]
\[ I_c = 69 \cdot 0.1 \, \text{mA} \]
\[ I_c = 6.9 \, \text{mA} \]

### Final Answers:
(i) Base current \( I_b = 0.1 \, \text{mA} \)
(ii) Collector current \( I_c = 6.9 \, \text{mA} \)

---