MCQ
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$L_s > L_m$
- ✓$L_s < L_m$
- C$L_s = L_m$
- DNone of these
✓
Answer
Correct option: B.
$L_s < L_m$
b
(b) As $\nu = \frac{c}{\lambda }$ ==> ${\nu _m} = \frac{c}{{{\lambda _m}}}$ and ${\nu _s} = \frac{c}{{{\lambda _s}}}$
$\because$ ( ${\lambda _m} > {\lambda _s}$ ==> ${\nu _m} < {\nu _s}$
Also ${\nu _m} = \frac{1}{{2\pi \sqrt {{L_m}C} }}$ and ${\nu _s} = \frac{1}{{2\pi \sqrt {{L_s}C} }}$
==> $\frac{{{\nu _m}}}{{{\nu _s}}} = \sqrt {\frac{{{L_s}}}{{{L_m}}}} $ ==> $Ls < Lm.$
(b) As $\nu = \frac{c}{\lambda }$ ==> ${\nu _m} = \frac{c}{{{\lambda _m}}}$ and ${\nu _s} = \frac{c}{{{\lambda _s}}}$
$\because$ ( ${\lambda _m} > {\lambda _s}$ ==> ${\nu _m} < {\nu _s}$
Also ${\nu _m} = \frac{1}{{2\pi \sqrt {{L_m}C} }}$ and ${\nu _s} = \frac{1}{{2\pi \sqrt {{L_s}C} }}$
==> $\frac{{{\nu _m}}}{{{\nu _s}}} = \sqrt {\frac{{{L_s}}}{{{L_m}}}} $ ==> $Ls < Lm.$
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