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A transmitting station transmits radiowaves of wavelength 360 m . Calculate the inductance of coil required with a condenser of capacity $1.20 \mu \mathrm{F}$ in the resonant circuit to receive them
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The correct answer is:
$3.07 \times 10^{-8} \mathrm{H}$
The frequency of radiowaves (speed $c=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ) transmitted
$f=\frac{c}{\lambda}=\frac{3 \times 10^8}{360}=8.3 \times 10^5 \mathrm{~Hz}$
Frequency of series resonant circuit
$\begin{aligned}f & =\frac{1}{2 \pi \sqrt{L C}} \\\text { or } \quad L & =\frac{1}{(2 \pi f)^2 C}\end{aligned}$
$\begin{aligned} & =\frac{1}{\left(2 \times 3.14 \times 8.3 \times 10^5\right)^2 \times 1.20 \times 10^{-6}} \\ & =3.07 \times 10^{-8} \mathrm{H}\end{aligned}$
$f=\frac{c}{\lambda}=\frac{3 \times 10^8}{360}=8.3 \times 10^5 \mathrm{~Hz}$
Frequency of series resonant circuit
$\begin{aligned}f & =\frac{1}{2 \pi \sqrt{L C}} \\\text { or } \quad L & =\frac{1}{(2 \pi f)^2 C}\end{aligned}$
$\begin{aligned} & =\frac{1}{\left(2 \times 3.14 \times 8.3 \times 10^5\right)^2 \times 1.20 \times 10^{-6}} \\ & =3.07 \times 10^{-8} \mathrm{H}\end{aligned}$
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