Question

If α = 0.98, I_co = 6 μA, & I_B = 100 μA for a transistor, then the value of I_C will be
1. 2.3 mA
2. 3.1 mA
3. 4.6 mA
4. 5.2 mA

Answer 1

Correct Answer - Option 4 : 5.2 mA

Concept:

For a BJT expression for collector current (I_c) is defined as-

I_C = β I_B + (1 + β) I_co

Where β = large signal current gain in CE mode of operation

I_C = collector current

I_co = collector current when emitter is open

I_B = Base current

α = large signal current gain in CB mode of operation

Relation between α and β:

\(\alpha = \frac{\beta }{{1 + \beta }}\;or\;\beta = \frac{\alpha }{{1 - \alpha }}\)

Calculation:

Given data: α = 0.98

I_co = 6 μA

I_B = 100 μA

\(\beta = \frac{\alpha }{{1 - \alpha }} = \frac{{0.98}}{{1 - 0.98}} = \frac{{0.98}}{{0.02}} = 49\)

I_c = β I_B + (1 + β) I_co

I_c = 49 × 100 + (49 + 1) 6 μA

I_c = 5200 μA

[ ∵ 1 μA = 10-6 A

1 mA = 10-3 A

1 mA = 103 μA ] 

I_c = 5.2 mA