A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 $$\mu$$A, it brings a change of 10 mA in collector current. If the load resistance is 2 k$$\Omega$$ and input resistance is 1 k$$\Omega$$. The value of power gain is $$x \times 10^4$$. The value of $$x$$ is ______.

A transistor in common emitter (CE) mode has the following parameters: change in base current $$\Delta I_B = 100\ \mu A = 100 \times 10^{-6}\ A$$, change in collector current $$\Delta I_C = 10\ mA = 10 \times 10^{-3}\ A$$, load resistance $$R_L = 2\ k\Omega = 2000\ \Omega$$ and input resistance $$R_i = 1\ k\Omega = 1000\ \Omega$$.

The current gain in CE configuration is defined as $$\beta = \frac{\Delta I_C}{\Delta I_B} = \frac{10 \times 10^{-3}}{100 \times 10^{-6}} = \frac{10^{-2}}{10^{-4}} = 100$$. The voltage gain of a CE amplifier is given by $$A_v = \beta \times \frac{R_L}{R_i}$$ and substituting the values yields $$A_v = 100 \times \frac{2000}{1000} = 100 \times 2 = 200$$. The power gain is the product of current gain and voltage gain: $$\text{Power gain} = \beta \times A_v = 100 \times 200 = 20000 = 2 \times 10^4$$. Alternatively, the power gain can also be expressed as $$\text{Power gain} = \beta^2 \times \frac{R_L}{R_i} = (100)^2 \times \frac{2000}{1000} = 10000 \times 2 = 20000 = 2 \times 10^4$$. Since the power gain is given as $$x \times 10^4$$, comparing with $$2 \times 10^4$$ gives $$x = 2$$.

Hence, the value of x is 2.