The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$ and $100 \mathrm{k} \Omega$ respectively, is shown in the figure. The Voltage and Power gain, are respectively :

(A) $5 \times 10^{4}, 2.5 \times 10^{6}$

(B) $5 \times 10^{4}, 5 \times 10^{6}$

(C) $5 \times 10^{4}, 5 \times 10^{5}$

(D) $2.5 \times 10^{4}, 2.5 \times 10^{6}$

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Semiconductors

The transfer characteristic curve of a transistor, having input and output resistance 100

Ω

and

100 k Ω

respectively, is shown in the figure. The Voltage and Power gain, are respectively :

Answer: (A)

From the transfer characteristic, a base-current change of

Δ I_{B} = 100 μ A

produces a collector-current change of

Δ I_{C} = 5 mA

, so the current gain is

β = \frac{Δ I _{C}}{Δ I _{B}} = \frac{5 \times 1 0 ^{- 3}}{100 \times 1 0 ^{- 6}} = 50

. The voltage gain is

A_{V} = β \frac{R _{out}}{R _{in}} = 50 \times \frac{100 \times 1 0 ^{3}}{100} = 5 \times 1 0^{4}

, and the power gain is

A_{P} = β A_{V} = 50 \times 5 \times 1 0^{4} = 2.5 \times 1 0^{6}

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option