Problem

In a certain circuit, the transistor has a collector current of $10 \, \mathrm{mA}$ and a base current of $40 \, \mu \mathrm{A}$. What is the current gain of the transistor?

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Data

• Collector current: $\mathrm{I}_{\mathrm{C}} = 10 \, \mathrm{mA} = 10 \times 10^{-3} \, \mathrm{A}$
• Base current: $\mathrm{I}_{\mathrm{B}} = 40 \, \mu \mathrm{A} = 40 \times 10^{-6} \, \mathrm{A}$

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Prerequisite Concepts

The current gain ($\beta$) of a transistor is defined as:

$$\beta = \frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}}$$

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Solution

Substitute the given values into the formula for $\beta$:

$$\beta = \frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}}$$ $$\beta = \frac{10 \times 10^{-3} \, \mathrm{A}}{40 \times 10^{-6} \, \mathrm{A}}$$ $$\beta = \frac{10}{0.04}$$ $$\beta = 250$$

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Answer

The current gain ($\beta$) of the transistor is $250$.