A transistor connected in common emitter mode, the voltage drop across the collector is 2 V and `beta` is 50, the base current if `R_C` is `2 kOmega` is

Options

A. `40 muA`
B. `20 muA`
C. `30 muA`
D. `15 muA`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given values
- Voltage drop across the collector (Vc) = 2 V
- Collector resistance (Rc) = 2 kΩ = 2000 Ω
- Current gain (β) = 50

### Step 2: Calculate the collector current (Ic)
Using Ohm's law, the collector current (Ic) can be calculated as:
\[ Ic = \frac{Vc}{Rc} \]

Substituting the values:
\[ Ic = \frac{2 \, \text{V}}{2000 \, \Omega} \]

Calculating:
\[ Ic = \frac{2}{2000} = 0.001 \, \text{A} = 1 \, \text{mA} \]

### Step 3: Relate Ic to Ib using the current gain (β)
The relationship between collector current (Ic) and base current (Ib) is given by:
\[ \beta = \frac{Ic}{Ib} \]

Rearranging this formula to find Ib:
\[ Ib = \frac{Ic}{\beta} \]

### Step 4: Substitute the values to find Ib
Substituting the values we have:
\[ Ib = \frac{1 \, \text{mA}}{50} \]

Calculating:
\[ Ib = \frac{0.001 \, \text{A}}{50} = 0.00002 \, \text{A} = 20 \, \mu\text{A} \]

### Final Answer
The base current (Ib) is **20 µA**.

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