Question

For a p-n-p transistor in CB configuration, the emitter current \[{{I}_{E}}\] is \[1\text{ mA}\] and \[\alpha =0.95\]. The base current and collector current are:
(A) \[0.95\text{ mA, 0}\text{.05 mA}\]
(B) \[0.05\text{ mA, 0}\text{.95 mA}\]
(C) \[9.5\text{ mA, 0}\text{.5 mA}\]
(D) \[0.5\text{ mA, 9}\text{.5 mA}\]

Answer 1

Hint:In a transistor, emitter current is equal to the sum of collector current and base current; and the common-base current gain \[\alpha \] is ratio of collector current to emitter current.
Formula used:
The common-base current gain \[\alpha \] is given by:
\[\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}\]
Here \[{{I}_{C}}\]implies the collector current and \[{{I}_{E}}\] implies the emitter-current.

Complete step by step answer:
The common-base current gain, \[\alpha =0.95\]
The emitter current, \[{{I}_{E}}=1\text{ mA}\]
Substitute the values \[\alpha =0.95\] and \[{{I}_{E}}=1\text{ mA}\] in the \[\alpha \]-formula to calculate collector current:
\[\begin{align}
& 0.95=\dfrac{{{I}_{C}}}{1\text{ mA}} \\
& {{I}_{C}}=0.95\text{ mA} \\
\end{align}\]
Therefore collector current is \[0.95\text{ mA}\]
In a transistor, emitter current is equal to the sum of collector current and base current, that is,
\[{{I}_{E}}={{I}_{B}}+{{I}_{C}}\] …..(i)
Where \[{{I}_{E}}\] is the emitter current, \[{{I}_{B}}\] is the base current and \[{{I}_{C}}\] is the collector current.
Substitute the value of \[{{I}_{C}}\] and \[{{I}_{E}}\] in equation (i):
\[\begin{align}
& 1\text{ mA}={{I}_{B}}+0.95\text{ mA} \\
& {{I}_{B}}=1\text{ mA}-0.95\text{ mA} \\
& {{I}_{B}}=0.05\text{ mA} \\
\end{align}\]
Therefore, base current is \[\text{0}\text{.05 mA}\].
Hence, option B is the correct answer.
Additional information:
 In a common emitter circuit, the change in collector current due to change in base current, causes a change in collector-emitter voltage and the voltage drop across the load resistor, because collector supply voltage is fixed.
In a transistor connected in CE mode input current is \[{{I}_{B}}\] and output current is \[{{I}_{C}}\].The d.c. current gain depends on the collector current and temperature.
The ratio of collector current to emitter current is called transistor alpha \[\alpha \]. Usually in god transistors \[\alpha \] ranges from \[0.98\] to \[0.988\].

Note:The common-base current gain has no unit as it is a ratio of two currents. Since emitter current is expressed in milliampere, so collector current and therefore base current also are expressed in milliampere.