Question

a transmitter consists of an lc circuit with an inductance of 15 μh and a capacitance of 23 pf. what is the wavelength of the electromagnetic waves it emits?
65 mm
5.6 m
35 m
29 mm
220 m

Explanation:

Step1: Calculate the resonant frequency \( f \) of the LC circuit

The formula for the resonant frequency of an LC circuit is \( f=\frac{1}{2\pi\sqrt{LC}} \).
Given \( L = 15\times10^{- 6}\text{ H}\) and \( C=23\times10^{-12}\text{ F}\).
Substitute the values into the formula:

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Step2: Calculate the wavelength \( \lambda \)

The speed of electromagnetic waves \( c = 3\times10^{8}\text{ m/s}\), and the relationship between \( c\), \( f\) and \( \lambda\) is \( c = f\lambda\), so \( \lambda=\frac{c}{f}\).
Substitute \( c = 3\times10^{8}\text{ m/s}\) and \( f = 8.5\times10^{6}\text{ Hz}\) into the formula:

$$ \lambda=\frac{3\times 10^{8}}{8.5\times10^{6}}\approx35\text{ m} $$

Answer:

35 m