Question

A transistor is connected in common emitter configuration. The collector supply is \(8 \mathrm{~V}\) and the voltage drop across a resistor of 800 in the collector circuit is \(0.5 \mathrm{~V}\). If the current gain factor \(\alpha\) is \(0.96\), then base current will be (A) \(27 \mu \mathrm{A}\) (B) \(26 \mu \mathrm{A}\) (C) \(25 \mu \mathrm{A}\) (D) \(24 \mu \mathrm{A}\)

Short answer

The short answer is (B) \(26 \mu \mathrm{A}\).

Step-by-step solution

Find the current flowing through the resistor

We are given the voltage drop across the resistor as 0.5 V, and the resistance as 800 Ω. We can use Ohm's Law to find the current flowing through the resistor: \(I = \frac{V}{R}\) Where I is the current, V is the voltage drop, and R is the resistance. Plug in the given values: \(I = \frac{0.5}{800} = 0.000625 \mathrm{~A}\)

Calculate the collector current

In a common emitter configuration, the current flowing through the resistor is the same as the collector current (Ic). Therefore, \(I_c = 0.000625 \mathrm{~A}\)

Use the current gain factor to find the base current

We are given the current gain factor α as 0.96. The relationship between α, base current (Ib), and collector current (Ic) can be expressed as: \(\alpha = \frac{I_c}{I_c + I_b}\) We can rearrange the equation to find the base current (Ib): \(I_b = \frac{I_c}{\alpha} - I_c\) Now, plug in the given values: \(I_b = \frac{0.000625}{0.96} - 0.000625 = 2.604 \times 10^{-5} \mathrm{~A}\)

Convert base current to microamperes and check the options

To convert the base current from amperes to microamperes, multiply by 10^6: \(I_b = 2.604 \times 10^{-5} \mathrm{~A} \times 10^6 = 26.04 \mu \mathrm{A}\) Checking the given options, we find that the closest answer to our calculation is: (B) \(26 \mu \mathrm{A}\)