1.

An ac source is connected to two circuits as shown Obtain current through resistance R at resonance in both the circuits .

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Solution :In sericse resonance impedance is minimum
`(as X_(L) = X_(C))` and equal to resistance
`Z =R`
`I = (V)/(Z) = (V)/( R)`
`L` and `C` are in parallel
`i_(1) = (V)/(X_(L)` lags voltage by `pi//2`
`i_(2) = (V)/(X_(C))` leads voltage by `pi//2`
`i = i_(2) -i_(1) = (V)/(X_(C) - (V)/(X_(L))`
`(V)/(Z) = (V')/(X_(C)) - (1)/(X_(L))`
At resonance, `X_(C) = X_(L)`
`(1)/(Z) = 0 implies Z =oo`
Impedance of overall circuit
`Z =R + oo = oo`
CURRENT through resistance `=0`

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