Question

For a common emitter circuit if ${{{I}_{C}}}/{{{I}_{E}}}\;=0.98$ then current gain for common emitter circuit will be
(A) $4.9$
(B) $98$
(C) $49$
(D) $9.8$

Answer 1

In a transistor, emitter current is equal to the sum of collector current and base current; and the current gain for the common-emitter circuit is ratio of collector current to base current.
Formula used:
The current gain $\beta$ for a common-emitter circuit is given by:
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$
Here ${{I}_{C}}$implies the collector current and ${{I}_{B}}$ implies the base-current.

Complete step by step answer:
The ratio of collector current to emitter current, $\dfrac{{{I}_{C}}}{{{I}_{E}}}=0.98$
So, ${{I}_{C}}=0.98{{I}_{E}}$
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 ${{I}_{C}}$ in equation (i):
${{I}_{E}}={{I}_{B}}+0.98{{I}_{E}}$…..(ii)
Rearrange equation (ii) to get the value of base current ${{I}_{B}}$ in terms of ${{I}_{E}}$ :

& {{I}_{E}}={{I}_{B}}+0.98{{I}_{E}} \\\ & {{I}_{B}}={{I}_{E}}-0.98{{I}_{E}} \\\ & {{I}_{B}}=0.02{{I}_{E}} \\\ \end{aligned}$$ Now, current gain, $$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$$ Substitute $${{I}_{C}}=0.98{{I}_{E}}$$ and $${{I}_{B}}=0.02{{I}_{E}}$$ in the current gain formula: $$\beta =\dfrac{0.98{{I}_{E}}}{0.02{{I}_{E}}}=49$$. Therefore, current gain for the common emitter circuit is $$49$$. Hence, option C is the correct answer. **Additional information:** In a common emitter circuit, the change in collector current due to change in base current, causes a change in collector-emitter voltage and the voltage drop across the load resistor, because collector supply voltage is fixed. In a transistor connected in CE mode input current is $${{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:** Always remember that current gain is the ratio of output current to the input current so it has no units.Most of the students get confused in it.