A wave of wavelength 300 m is to be radiated through a transmitter. You are given a capacitor of `2.5 muF`. What should be the value of the inductance of the coil required to produce the oscillatory circuit? [Take `pi^(2)=10`]

Options

A. `10^(-6) H`
B. `10^(-8) H`
C. `2 xx 10^(-7) H`
D. `3 xx 10^(-8) H`

Answer

B

Explanation

The oscillating frequency,
`f = 1/(2pisqrt(LC)) :. f^(2) = 1/(4pi^(2)Lc)`
`:. L = 1/(4 pi^(2)f^(2)c)` .....(i)
But `f = ("velocity of light(c)")/("wavelength(lambda)")`
`:. F^(2) = (c^2)/(lambda^2) = (3 xx 10^(8) xx 3 xx 10^(8))/(300 xx 300) = 10^(12)`
`:.` From (1) :. L = (1)/(4 xx 10 xx 10^(12) xx 2.5 xx 10^(-6))`
`:. L = 1/(10^(+8)) = 10^(-8)H`.