Question

The current amplification factor and the collector current in a transistor circuit are 100 and 2.2 mA respectively. Then the base current is

• A. $0.22 \ \mu\text{A}$
• B. $22 \ \mu\text{A}$
• C. $220 \ \mu\text{A}$
• D. $2.2 \ \mu\text{A}$

Hint:

Transistor Current Relationships

• $\beta = \fracI_CI_B$
• $I_E = I_B + I_C$
• Typical $\beta$ values: 50–300
• Always convert mA to A before calculations.

Answer 1

The Correct Option is B

In CE (Common Emitter) configuration: \[ \beta = \frac{I_C}{I_B} \Rightarrow I_B = \frac{I_C}{\beta} \] Given: \[ I_C = 2.2\ \text{mA} = 2.2 \times 10^{-3}\ \text{A},\ \beta = 100 \Rightarrow I_B = \frac{2.2 \times 10^{-3}}{100} = 2.2 \times 10^{-5}\ \text{A} \] \[ I_B = 22\ \mu\text{A} \] Thus, option (2) is correct.

Answer 2

Step 1: Understand the given parameters and the transistor operation
In a transistor, the current amplification factor (β) indicates how much the base current (I_B) is amplified to produce the collector current (I_C). Given β = 100, it means the collector current is 100 times the base current.

Step 2: Write down the relationship between collector current and base current
The fundamental equation relating collector current (I_C), base current (I_B), and current amplification factor (β) is:
β = I_C / I_B
This means the collector current depends directly on the base current and the amplification factor.

Step 3: Rearranging the formula to find base current
To find the base current, rearrange the formula:
I_B = I_C / β
This allows calculation of the small input current required at the base to produce the desired collector current.

Step 4: Substitute the known values
Given:
I_C = 2.2 mA = 2.2 × 10⁻³ A
β = 100
Calculating:
I_B = (2.2 × 10⁻³) / 100 = 2.2 × 10⁻⁵ A

Step 5: Convert base current into microamperes for practical understanding
Since 1 A = 10⁶ μA,
I_B = 2.2 × 10⁻⁵ A = 2.2 × 10⁻⁵ × 10⁶ μA = 22 μA
This shows the base current is very small compared to the collector current, highlighting the transistor's amplification property.

Step 6: Interpretation and conclusion
The transistor effectively amplifies the input base current of 22 μA to a collector current of 2.2 mA, demonstrating the usefulness of β in designing transistor circuits. Knowing this helps in understanding transistor operation and in calculating currents for circuit design.
Hence, the base current is 22 μA.