Question
Question: The current gain in a common base circuit is 40. The ratio of emitter current to base current is ...
The current gain in a common base circuit is 40. The ratio of emitter current to base current is
A. 40
B. 41
C. 42
D. 43
Solution
As we all know that the common base amplifier is one of the types of Bipolar junction transistor where the terminal’s base is the common base for both the output and the input signals. It is used with the amplifier having fewer impedance levels.
Complete step by step answer:
It is given to us that the current gain, β=40.
We will now express the current amplification factor in terms of current gain. So, we can say that,
α=1+ββ ………...… (I)
Here, α is the current amplification factor, and β is the current gain factor.
We can now substitute the value of β=40in equation (I) to find the value of α. So we get,
⇒α=1+4040
⇒α=4140
We will now write the expression for α and β in terms of collector current, base current and emitter current as,
β=IbIc
Here, Ic and Ib are the collector and base currently respectively.
We will solve it further and it gives,
⇒Ic=βIb …………... (II)
Similarly, we can say that,
α=IeIc
Here, Ie is the emitter current.
We will solve it further and it will give,
⇒Ic=Ieα ……………. (III)
We will now equate equation (II) and equation (III) since both are the terms of collector current. Hence, we will get,
Ieα=Ibβ
⇒IbIe=αβ ………………... (IV)
We can now substitute.α=4140 and β=40 in equation (IV) to find the required value of IbIe
⇒IbIe=414040=4040×41
∴IbIe=41
Therefore, we can see that the ratio of emitter current to base current is 41. Hence, the correct option is (B).
Note:
We must know that the input impedance of the common base circuit is too less for most source signals and it very strongly depends on collector current i.e. for 1mA, it is about 26Ω and for 2mA it is about 13Ω.