Question

In a radio receiver, the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively then

• A. L_s > L_m
• B. L_s < L_m
• C. L_s = L_m
• D. None of these

Answer 1

The correct option is B L_s < L_m

As v = $\frac{c}{\lambda }\Rightarrow v_m=\frac{c}{{\lambda }_m}$ and $v_s=\frac{c}{{\lambda }_s}$
$\because {\lambda }_m>{\lambda }_s\Rightarrow v_m<v_s$
Also $v_m=\frac{1}{2\pi \sqrt{L_{m}C}}$ and $v_s=\frac{1}{2\pi \sqrt{L_{s}C}}$
$\Rightarrow \frac{v_m}{v_s}=\sqrt{\frac{L_s}{L_m}}\Rightarrow L_s<L_m$.