The current gain of a BJT is — Analog Electronics MCQ

Answer: Option C

Solution:

Option A: $g_{m} r_{o}$ is incorrect because this expression represents the voltage gain in a transistor, not the current gain. The term

r_{o}

is the output resistance, and multiplying

g_{m}

(transconductance) with

r_{o}

gives the voltage gain, not the current gain.

Option B: $\frac{g _{m}}{r _{o}}$ is incorrect because this expression represents the inverse relationship between transconductance and output resistance, which is related to the voltage gain of the amplifier, not the current gain.

Option C: $g_{m} r_{π}$ is correct because this is the standard expression for the current gain of a BJT in terms of the transconductance (

g_{m}

) and the base-emitter resistance (

r_{π}

). The current gain is the product of these two parameters.

Option D: $\frac{g _{m}}{r _{π}}$ is incorrect because this expression does not correctly represent the current gain of a BJT. Instead, it gives a ratio that relates to the voltage gain and other characteristics of the transistor, but not the current gain.

Conclusion: The correct answer is Option C:

g_{m} r_{π}

because the current gain of a BJT is given by the product of transconductance (

g_{m}

) and base-emitter resistance (

r_{π}