Question

A transmitting station transmits radiowaves of wavelength $360\, m$. Calculate the inductance of coil required with a condenser of capacity $1.20\, \mu F$ in the resonant circuit to receive them

• A. $3.07 \times 10^{-8} H$
• B. $2.07 \times 10^{-8} H$
• C. $4.07 \times 10^{-8} H$
• D. $60.7 \times 10^{-8} H$

Answer 1

Answer: (A)

The frequency of radiowaves (speed $c=3 \times 10^{8} m / s$) transmitted
$f=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{360}=8.3 \times 10^{5} Hz$
Frequency of series resonant circuit
$f =\frac{1}{2 \pi \sqrt{L C}}$
or $L =\frac{1}{(2 \pi f)^{2} C}$
$=\frac{1}{\left(2 \times 3.14 \times 8.3 \times 10^{5}\right)^{2} \times 120 \times 10^{-6}}$
$=3.07 \times 10^{-8} H$