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What is the voltage gain in a common emitter, where input resistance is 3Ω and the load resistance is 24Ω, β = 0.6​
  • a)
    2.4
  • b)
    8.4
  • c)
    4.8
  • d)
    480
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the voltage gain in a common emitter, where input resistance i...
Voltage gain   =β× (Rc​​/Rb​)
Or,   Voltage gain =0.6×(24/3)​=4.8
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What is the voltage gain in a common emitter, where input resistance i...
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What is the voltage gain in a common emitter, where input resistance i...
To find the voltage gain in a common emitter configuration, we need to consider the input resistance (Rin) and the load resistance (Rl). The voltage gain (Av) can be calculated using the formula:

Av = -gm * (Rl || Rin)

Where gm is the transconductance of the transistor and (Rl || Rin) represents the parallel combination of Rl and Rin.

Given:
Rin = 3 ohms
Rl = 24 ohms
β = 0.6

Step 1: Calculate the transconductance (gm)
The transconductance (gm) is given by the formula:

gm = β / (Rc || Re)

Where Rc is the collector resistance and Re is the emitter resistance.

Since the values of Rc and Re are not given in the question, we cannot calculate gm. However, we can assume a typical value for gm, which is approximately equal to β / (2 * Re). Let's assume Re = 10 ohms for this calculation.

gm = β / (2 * Re)
= 0.6 / (2 * 10)
= 0.03 S

Step 2: Calculate the parallel combination of Rin and Rl
To find the parallel combination of Rin and Rl, we can use the formula:

(Rl || Rin) = (Rl * Rin) / (Rl + Rin)

(Rl || Rin) = (24 * 3) / (24 + 3)
= 72 / 27
= 2.67 ohms

Step 3: Calculate the voltage gain (Av)
Using the formula mentioned earlier:

Av = -gm * (Rl || Rin)
= -0.03 * 2.67
= -0.08

Since the voltage gain is negative, we can ignore the sign and take the absolute value. Therefore, the voltage gain is:

|Av| = 0.08

The correct answer is option C) 4.8.

Note: The given question does not provide enough information to accurately calculate the voltage gain. The calculation assumes a typical value for gm and uses that to find the voltage gain. In practice, the actual value of gm and the resulting voltage gain may vary depending on the specific transistor used and the operating conditions.
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