Transistor As Amplifier

Question

A common-emitter transistor amplifier has a base current of 20 microampere and a collector current of 2 milliampere in its active region.

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NCERT defines the common-emitter current gain, beta, as the ratio of the collector current to the base current in the active region, written $\beta = \frac{I_C}{I_B}$. This parameter measures how effectively a small base current controls a much larger collector current, which is the basis of transistor amplification. Converting to consistent units, the collector current is $2$ mA $= 2000$ microampere and the base current is $20$ microampere, so $\beta = \frac{2000}{20} = 100$. The value 40 is wrong because it does not follow from the given currents and appears to mix up unrelated numbers. The value 0.01 is wrong because it inverts the ratio, dividing base current by collector current, which instead gives a fraction far less than one. The value 2000 is wrong because it forgets to divide by the base current and simply reports the collector current in microampere. As stated in NCERT Class 12, Chapter 14, beta is the ratio of collector to base current and typically ranges from tens to a few hundred. A magnitude check confirms that a base current five hundred times smaller than the collector current is impossible here, whereas a factor of one hundred is entirely typical for a real transistor.

Transistor As Amplifier

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