Question

Consider a common-emitter current gain of β = 150 and a base current of i_B = 15 μA. If the transistor is biased in the forward active mode, the collector and emitter current will be
1. 2.25 mA and 2.27 mA
2. 3.25 mA and 2.27 mA
3. 2.25 mA and 1.37 mA
4. 3.25 mA and 1.37 mA

Answer 1

Correct Answer - Option 1 : 2.25 mA and 2.27 mA

Concept:

The common base DC current gain is a ratio of the value of the transistor's collector current to the value of the transistor's emitter current, i.e.

\(α = \frac{{{I_c}}}{{{I_e}}}\)   ---(1)

Also, the common-emitter current gain is the ratio of the value of the transistor's collector current to the value of the transistor's base current in a transistor, i.e.

\(β = \frac{{{I_c}}}{{{I_b}}}\)   ---(2)

Using Equation (1) and (2), we get:

\(β =\frac{α}{1-α}\)

For a transistor, the relation between the collector, base, and emitter current is:

IE = IB + IC

IC = β IB

IE = (β + 1) IB

Calculation:

With β = 150 and base current iB = 15 μA, the collector current will be:

IC = β IB = 150 × 15 μA

I_C = 2250 μA

I_C = 2.25 mA

The emiiter current will be:

IE = (β + 1) IB = (150 + 1) 15 μA

I_E = 151 × 15 μA

I_E = 2.265 mA