Question

A transistor is operated in common emitter configuration at constant collector voltage V_C = 1.5 V such that a change in the base current from 100 µA to 150 µA produces a change in the collector current from 5 mA to 10 mA. The current gain (β) is :

• A. 50
• B. 70
• C. 100
• D. 125

Answer 1

The Correct Option is C

To determine the current gain (β) of a transistor in a common emitter configuration, we need to understand the relationship between the base current (\(I_B\)) and the collector current (\(I_C\)). The current gain (\( \beta \)) is defined as the ratio of the change in collector current to the change in base current. Mathematically, this can be expressed as:

\(\beta = \frac{\Delta I_C}{\Delta I_B}\)

Let's apply this formula to the given data:

1. The change in base current \( (\Delta I_B) \) is from 100 µA to 150 µA, giving us:

\(\Delta I_B = 150 \, \mu A - 100 \, \mu A = 50 \, \mu A \)

2. The change in collector current \( (\Delta I_C) \) is from 5 mA to 10 mA, giving us:

\(\Delta I_C = 10 \, mA - 5 \, mA = 5 \, mA \)

We must convert these currents into the same unit for accurate calculations. Convert microamperes to milliamperes:

• \(1 \, \mu A = 0.001 \, mA\)

So,

• \(\Delta I_B = 50 \, \mu A = 0.050 \, mA\)

Now we can calculate \( \beta \):

\(\beta = \frac{\Delta I_C}{\Delta I_B} = \frac{5 \, mA}{0.050 \, mA} = 100 \)

Therefore, the current gain (\(\beta\)) is 100.

This confirms that the correct option is 100.