Question

In a transistor circuit, when the base current is increased by 50 micro-amperes keeping the collector voltage fixed at 2 volts, the collector current increases by 1 mA. The current gain of the transistor is
(A) 20
(B) 40
(C) 60
(D) 80

Answer 1

Hint: The current amplification factor or current gain is the ratio of the collector current to the base current. We have given both the collector current and base current. Simply substitute the values and you will get the desired answer.

Formula used:
\[\beta = \dfrac{{{I_C}}}{{{I_B}}}\]
Here, \[{I_C}\] is the collector current and \[{I_B}\] is the base current of the transistor.

Complete step by step answer:
We have given that the base current increased by \[50\,\mu A\] then collector current increases by 1 mA.
We know that the current amplification factor or current gain is the ratio of the collector current to the base current. Therefore,
\[\beta = \dfrac{{{I_C}}}{{{I_B}}}\]
Here, \[{I_C}\] is the collector current and \[{I_B}\] is the base current of the transistor.
We substitute \[50\,\mu A\] for \[{I_B}\] and 1 mA for \[{I_C}\] in the above equation.
\[\beta = \dfrac{{{{10}^{ - 3}}\,A}}{{50 \times {{10}^{ - 6}}\,A}}\]
\[ \therefore \beta = 20\]

Therefore, the current gain of the transistor is 20.So, the correct answer is option (A).

Additional information:
The physical construction of the transistor determines the relationship between base current, collector current and emitter current. Therefore, if we change the base current slightly, it will result in large change in the collector current depending upon the current amplification factor. The typical value of the current gain lies between 20 and 200 for most of the transistors. If we have the transistor if current gain 100 that means there is 1 electron in base of the transistor for the flow of 100 electrons between collector and emitter.

Note: To use the formula, \[\beta = \dfrac{{{I_C}}}{{{I_B}}}\], both collector current and base current should have the same unit. While solving these types of questions, if emitter current is given instead of base current, then students should determine \[\alpha \] that is the ratio of the collector current to the emitter current. The relation between these two ratios is \[\beta = \dfrac{\alpha }{{\alpha - 1}}\].