Question

An LC circuit with a 4.91 pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.3 m. a) What is the resonant frequency? 90909090.9090909 Hz b) What inductance is in series with the capacitor? 0.56748 uH

Answer 1

(a) Since the formula of frequency is that,

$f = \frac{c}{\lambda}$

hence the resonant frequency of LC circuit is that,

$f = \frac{c}{\lambda} = \frac{3 \times 10^8}{3.3}$

Hz

hence the resonant frequency is f = 90909090.91 Hz.

(b) since the formula of resonant frequency of LC circuit is,

$f = \frac{1}{2 \pi} \frac{1}{\sqrt{LC}}$

$\Rightarrow$   $L = \frac{1}{4 \pi^2 f^2C}$

$\Rightarrow L = \frac{1}{4 \pi^2 (90909090.91)^2 \times 4.91 \times 10^{-12}}$

$\Rightarrow L = 6.242292 \times 10^{-7}$ Henry

$\Rightarrow L = 0.6242292$ micro Henry

$\Rightarrow L = 0.6242292$$\mu H$

hence the inductance is in series with the capacitor is L = 0.6242292 $\mu H$