JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Semiconductors

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by

100 μ A

, it brings a change of 10 mA in collector current. If the load resistance is

2 k Ω

and input resistance is

1 k Ω

, the value of power gain is

x \times 1 0^{4}

. The value of x is ____.

Answer: 2

Solution

The current gain

β

is:

β = \frac{Δ i _{C}}{Δ i _{B}} = \frac{10 \times 1 0 ^{- 3}}{100 \times 1 0 ^{- 6}} = 100

The power gain in a common emitter amplifier is:

Power gain = β^{2} \times \frac{R _{0}}{R _{in}}

Substituting

β = 100

R_{0} = 2 k Ω

, and

R_{in} = 1 k Ω

Power gain = (100)^{2} \times \frac{2}{1} = 10000 \times 2 = 2 \times 1 0^{4}

Therefore,

x = 2

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Integer answer