Question

The current gain $\left( \beta \right)$ of a transistor in a common base mode is $40$ . To change the collector current by $160\,mA$ , the necessary change in the base current is (at constant ${V_{CE}}$ )
A) $0.25\,\mu$
B) $4\,\mu A$
C) $4\,mA$
D) $40\,mA$

Answer 1

Use the formula of the current gain and rearrange it to obtain the value of the change in the base current. Substitute the values of the current gain and the change in the collector current of the transistor, in the rearranged formula to know the answer.

Useful formula:
The formula of the current gain is given by
$\beta = \dfrac{{\Delta {I_c}}}{{\Delta {I_b}}}$
Where $\beta$ is the current gain of the transistor, $\Delta {I_c}$ is the change in the collector current and the $\Delta {I_b}$ is the change in the base current.

Complete step by step solution:
It is given that the
Current gain of the transistor in the common base mode, $\beta = 40$
The change in the collector current, $\Delta {I_c} = 160\,mA$
By using the formula of the current gain,
$\beta = \dfrac{{\Delta {I_c}}}{{\Delta {I_b}}}$
By rearranging the above formula, in order to obtain the value of the change in the base current,
$\Delta {I_b} = \dfrac{{\Delta {I_c}}}{\beta }$
Substituting the values of the change in the collector current and the change in the collector current given in the question in the above equation,
$\Delta {I_b} = \dfrac{{160\,mA}}{{40}}$
By performing the basic arithmetic division, the result obtained is
$\Delta {I_b} = 4\,mA$
Hence the change in the base current is obtained as $4\,mA$ .

Thus the option (C) is correct.

Note: The current gain of the transistor in the common base mode shows that the small change in the base current can cause the greater changes in the collector current of the transistor. The value of the current can be maximum up to $200$in case of the standard transistor.