Question

A transmitter consists of LC circuit with an inductance of 1 μH and a capacitance of 1 μF. What is the wavelength of the electromagnetic waves it emits?

Answer 1

Inductance of LC circuit, L = 1 μH = 1 × 10^-6 H

Capacitance of LC circuit, C = 1 μF = 1 × 10^-6 F

Wave length of the electromagnetic wave X = λ = ${\displaystyle \frac{\text{C}}{\text{f}}}$

Velocity of light C = 3 x 10⁸ ms^-1

Frequency of electromagnetic wave, f = ${\displaystyle \frac{1}{2\pi \sqrt{\text{LC}}}}$

${\displaystyle =\frac{1}{2\times 3.14\sqrt{1\times {10}^{-6}\times {10}^{-6}}}}$

${\displaystyle =\frac{1}{6.28\times {10}^{-6}}}$

${\displaystyle \Rightarrow \text{f}=15.92\times {10}^4}$ Hz

Wave length λ = ${\displaystyle \frac{\text{C}}{\text{f}}=\frac{3\times {10}^8}{15.92\times {10}^4}}$

= 0.1884 × 10⁴

λ = 18.84 × 10² m