Read the following passage and then answer questions on the basis of your under standing of the passage and the related studied concepts. Passage: For an LCR series circuit driven with an alternating voltage of amplitude Vmand angular frequency oo, the current amplitude is given as
`I_(m) =V_(m)/z = V_(m)/sqrt(R^(2) + (X_(L)-X_(C))^(2)) =V_(m)/sqrt(R^(2) + (Iomega -1/(c omega))^(2))`
If `omega` is varied then for a particular frequency `omega_(0), X_( C) = X_(L)` and then Z = R and hence, `I_(m) = V_(m)/R` is maximum. This frequency is called the resonant frequency. The resonant frequency `omega_(0) = 1/sqrt(LC)` = Resonance of a LCR series a.c. circuit is said to be sharping current amplitude Im falls rapidly on increasing/decreasing the angular frequency from its resonant value 0. Mathematically, sharpness of resonance is measured by the quality factor of the circuit, which is given as:
`Q = (omega L)/R = 1/R sqrt(L/C)`
(d) How is a resonant circuit is utilised to tune a TV set at a particular channel ?

Explanation

Signals of different TV stations are received at different frequencies. The antenna of a TV set receives these signals and drives a current in the tuning circuit. However, only the signal corresponding to the resonant frequency is able to drive appreciable current and is further processed. When we tune a TV, we change the capacitance of the tuning circuit and hence the resonant frequency changes. When this frequency matches with the frequency of the signal from the desired TV channel, the tuning is complete.