Question

An LC- circuit (inductance 0.01 H and capacitance `1 muF`) is connected to a variable a.c. source as shown in fig. 14.8. Draw rough sketch of the current -variation as the frequency is changed from 1 kHz to 2 kHz.

Answer 1

`(1)/(Z) = (1)/(X_C) - (1)/(X_(L))`
At resonace `X_(L) = X_(C)`
`omegaL = (1)/(omegaC) implies omega = omega_(r) = (1)/(sqrt(LC)`
`f_(r) = (omegar)/(2pi) = (1)/sqrt(2pi ) = (1)/(2pi sqrt(LC)) = (1)/(2pisqrt((0.01) xx 10^(-6)))`
` =1592 Hz = 1.592 kHz`
`At f = _(r)` Current is minimum and equal to zero
`f lt f_(r), X_(C) gt X_(L)` as frequency increases increases impedance increases
`f = f_(r), X_(C) gt X_(L)` impedance is maximum `Z = oo`
`f gt f_(r), X_(C) lt X_(L)` as frequency increases, impedance decreases .
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