
The relationship between current gain in Common Base [CB] mode and current gain in Common Emitter [CE] mode is
A.
B.
C.
D.
Answer
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Hint:Use the formulae for the current gain in Common Base mode and current gain in Common Emitter mode. Also use the relation between the emitter current, collector current and base current. Substitute the values of the current gains in Common Base mode and Common Emitter mode in this relation and solve it.
Formulae used:
The current gain in Common Base [CB] mode is given by
…… (1)
Here, is the current from the collector and is the current form emitter.
The current gain in Common Emitter [CE] mode is given by
…… (2)
Here, is the current from the collector and is the current form base.
Complete step by step answer:
We have asked to determine the relationship between the current gain in Common Base [CB] mode and the current gain in Common Emitter [CE] mode.From equation (1). We can write
From equation (2). We can write
We know that in a transistor the sum of the current from the collector and the current from base is equal to the current from the emitter.
Multiply both sides of the above equation by the collector current .
Substitute for and for in the above equation.
Therefore, the relationship between the current gain in Common Base [CB] mode and the current gain in Common Emitter [CE] mode is .
Hence, the correct option is B.
Note: The students should be careful while using the formulae for the current gain in Common Base mode and Common Emitter mode. If the ratio of the currents in these formulae is taken incorrectly then we will also end with the incorrect relation between the current gain in Common Base and Common Emitter mode.
Formulae used:
The current gain
Here,
The current gain
Here,
Complete step by step answer:
We have asked to determine the relationship between the current gain
From equation (2). We can write
We know that in a transistor the sum of the current from the collector and the current from base is equal to the current from the emitter.
Multiply both sides of the above equation by the collector current
Substitute
Therefore, the relationship between the current gain
Hence, the correct option is B.
Note: The students should be careful while using the formulae for the current gain in Common Base mode and Common Emitter mode. If the ratio of the currents in these formulae is taken incorrectly then we will also end with the incorrect relation between the current gain in Common Base and Common Emitter mode.
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