Question

A resonant circuit in a radio receiver is tuned to a certain station when the inductor has a value of 0.263 mH and the capacitor has a value of 29.1 pF. Calculate the frequency of the radio station. Tries 0/20 What is the wavelength of the radiowaves emited by the radio station?

Answer 1

Answer:

1.82 x 10⁶ Hz

164.84 m

Explanation:

L = Inductance of the inductor = 0.263 mH = 0.263 x 10⁻³ H

C = Capacitance of the capacitor = 29.1 x 10⁻¹² F

f = frequency of radio station

At resonance, we know that

$2\pi fL = \frac{1}{2\pi fC}$

$2(3.14)(0.263\times 10^{-3})f = \frac{1}{2(3.14)(29.1\times 10^{-12}) f}$

f = 1.82 x 10⁶ Hz

v = speed of radio wave = 3 x 10⁸ m/s

λ = wavelength of radio wave

Using the equation

v = f λ

3 x 10⁸ = (1.82 x 10⁶) λ

λ = 164.84 m