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 = `"C"/"f"`

Velocity of light C = 3 x 10⁸ ms^-1

Frequency of electromagnetic wave, f = `1/(2pi sqrt"LC")`

`= 1/(2 xx 3.14 sqrt(1 xx 10^-6 xx 10^-6))`

`= 1/(6.28 xx 10^-6)`

`=> "f" = 15.92 xx 10^4` Hz

Wave length λ = `"C"/"f" = (3 xx 10^8)/(15.92 xx 10^4)`

= 0.1884 × 10⁴

λ = 18.84 × 10² m