A transistor is used in common-emitter mode in an amplifier circuit. When a signal of $$10$$ mV is added to the base-emitter voltage, the base current changes by $$10\mu$$A and the collector current changes by $$1.5$$ mA. The load resistance is $$5$$ k$$\Omega$$. The voltage gain of the transistor will be ______.

A transistor in common-emitter mode has the following parameters: change in base-emitter voltage $$\Delta V_{BE} = 10$$ mV, change in base current $$\Delta I_B = 10 \mu$$A, change in collector current $$\Delta I_C = 1.5$$ mA, and load resistance $$R_L = 5$$ k$$\Omega$$.

Calculate the current gain $$\beta$$: $$ \beta = \frac{\Delta I_C}{\Delta I_B} = \frac{1.5 \times 10^{-3}}{10 \times 10^{-6}} = \frac{1.5 \times 10^{-3}}{10^{-5}} = 150 $$

Calculate the input resistance $$R_i$$: $$ R_i = \frac{\Delta V_{BE}}{\Delta I_B} = \frac{10 \times 10^{-3}}{10 \times 10^{-6}} = \frac{10^{-2}}{10^{-5}} = 1000 \text{ } \Omega = 1 \text{ k}\Omega $$

Calculate the voltage gain: $$ A_v = \beta \times \frac{R_L}{R_i} = 150 \times \frac{5 \times 10^3}{1 \times 10^3} = 150 \times 5 = 750 $$

The voltage gain of the transistor is 750.