Semiconductor Devices

The question tells us that the voltage gain divided by the current amplification factor ( $\beta$ ) equals 4.We know that the formula for voltage gain in a common emitter amplifier is $A_V = \; \frac{\beta \times R_C}{R_B}$, where $R_C$ is collector resistance and $R_B$ is base resistance.So if we divide $A_V$ by $\beta$, we get:$\frac{A_V}{\beta} = \frac{ \; \frac{\beta \times R_C}{R_B} }{\beta}$This simplifies to:$\frac{R_C}{R_B}$The question gives $\frac{A_V}{\beta}=4$, so:$\frac{R_C}{R_B}=4$This means the ratio of collector resistance to base resistance is $4: 1$.