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An LC circuit (L = 0.01H, C = 1muF) is c...

An LC circuit `(L = 0.01H, C = 1muF)` is connected to an AC source of variable frequency. If the frequency is varied from 1 kHz, then show the consequent variation of impedance by a rough sketch.

Text Solution

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Impedance (Z) of the circut is
`1/Z = 1/X_(c) - 1/X_(L)`
At resonance, `X_(L)=X_(C)`
`rArr omegaL=1/(omegaC)`
`rArr omega=omega_(0)=1/(sqrt(LC))`
`rArr f_(0) = omega_(0)/(2pi)=1/(2pisqrt(LC))`
`=1/(2pisqrt(0.01 xx 10^(-6)))`
=1592 Hz=1.592 kHz
At `f=f_(0)`, impedance is minimum and equal to zero.
At `fltf_(0)`, `X_(C)gtX_(L)`, as frequency increases, impedance increases
`f=f_(0),X_(C)gtX_(L)`, as frequency increases, impedance decreases as shown below
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