Question:

In a transistor amplifier, the two AC current gains $\alpha $ and $ \beta $ are defined as $\alpha=\frac{\partial I_C}{\partial I_E} $ and $ \beta =\frac{\partial I_C}{\partial I_B}$ the relation between $\alpha$ and $\beta$ is

Updated On: Apr 30, 2024

$\beta=\frac{1-\alpha}{\alpha}$
$\beta=\frac{\alpha}{1-\alpha}$
$\beta=\frac{\alpha}{1+\alpha}$
$\beta=\frac{1+\alpha}{\alpha}$

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The Correct Option is B

Solution and Explanation

Given, $\alpha=\frac{\partial I_C}{\partial I_E} $ and $ \beta=\frac{\partial I_C}{\partial I_B}$
We know that in a transistor amplifier
$ I_E =I_C +I_B \Rightarrow \partial I_E =\partial I_C +\partial I_B$
Now, $ \beta=\frac{\partial I_C}{\partial I_B}$
$ =\frac{\partial I_C}{\partial I_E - \partial I_C}$
$ =\frac{\partial I_C / \partial I_E}{1-\partial I_C /\partial I_E} $
$\therefore \beta=\frac{\alpha}{1-\alpha}$

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Concepts Used:

Semiconductors

Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.

Properties of Semiconductor:

Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
Lesser power losses.

Uses of Semiconductor:

Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.