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

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:

& 0.95=\dfrac{{{I}_{C}}}{1\text{ mA}} \\\ & {{I}_{C}}=0.95\text{ mA} \\\ \end{aligned}$$ Therefore collector current is $$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{aligned} & 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{aligned}$$ Therefore, base current is $$\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.