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

Hint: 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 \[{{I}_{E}}\] :
\[\begin{align}
& {{I}_{E}}={{I}_{B}}+0.98{{I}_{E}} \\
& {{I}_{B}}={{I}_{E}}-0.98{{I}_{E}} \\
& {{I}_{B}}=0.02{{I}_{E}} \\
\end{align}\]
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.