A transmitter consists of `I_(C )` circuit with an inductance of 1 `mu`H and a capacitance of 1 `mu`F. What is the wavelength of the electromagnetic waves it emits?

Explanation

An inductance of LC circuit L = `1 mu"H" = 1 xx 10^(-6) `H
Capacitance of LC circuit C = `1 mu`F = `1 xx 10^(-6)` F
To find:
Wavelength of e.m. wave emitted `lambda` = ?
Formula :
`lambda = (c )/(lambda) rArr = (c )/(lambda)`
the velocity of light in vacuum, C = `3 xx 10^(8) ms^(-1)`
the frequency of e.m. wave `lambda = (1)/(2 pi sqrt(LC))`
Solution :
`therefore lambda = (c )/((1)/(2)cdot (1)/(pi sqrt(LC))) = 2pi sqrt(LC) xx c`
`= 2 xx 3.14 sqrt(10^(-6) xx 10^(-6) ) xx 3 xx 10^(8)`
`lambda = 6.25 xx 10^(-6) xx 3 xx 10^(8)`
`lambda = 18.84 xx 10^(2) m`