Physics - Semiconductors Question with Solution | TestHub

Given:
Output resistance, $R_{out}=500\text{ k}\Omega =5\times 10^5\Omega$
Current gain, $\beta =50$
Power gain, $A_p=5\times 10^6$

The power gain of a common emitter amplifier is given by the formula:
$A_p={\beta }^2\times \frac{R_{out}}{R_{in}}$

Rearranging the formula to solve for input resistance $R_{in}$:
$R_{in}=\frac{{\beta }^2\times R_{out}}{A_p}$

Substituting the given values:
$R_{in}=\frac{(50{)}^2\times 5\times 10^5}{5\times 10^6}$

$R_{in}=\frac{2500\times 5\times 10^5}{5\times 10^6}$

$R_{in}=\frac{2500}{10}$

$R_{in}=250\Omega$

Answer: $250\Omega$