Question

Draw a curve for showing variation in alternating current with frequency in `LCR` resonant circuit.Hence obtain an expression of bandwidth.

Answer 1

There are two half power frequencies `f_(1)` and `f_(2)`:
(a)Lower half power frequency `(f_(1))`:
This half power frequency is less than the resonant frequency `f_(r)`, At this frequency the circuit is capacitive.
(b )Upper half power frequency `(f_(2))`:
This half-power is greater than the resonant frequency `f_(r)`.At this frequency the circuit is inductive.
Band width `(Deltaf)`:
The difference of half-power frequencies `f_(1)` and `f_(2)` is called band-width `(Deltaf)`
Band width `Deltaf=(f_(2)-f_(1))`
For series resonant circuit :
`Deltaf=1/(2pi) (R/L)`