A circuit consisting of a capacitor and a coil connected in seried if fed two alternating voltages of equal amplitudes but different frequencies. The frequency of one voltage is equal to the natural oscillation frequency `( omega_(0))` of the circuit, the frequency of the other voltage is `eta` times highter. Find the ratio of the current amplitudes `(I_(0)//I)` generated by the two voltages if the quality factor of the system is equal to `Q`. Calculate this ratio for `Q=10` and `100,` if `eta=1.10`.

Explanation

At resonance ` omega= omega_(0)`
`I_(m) ( omega_(0))=(V_(m))/( R)`
Then `I_(m)(etaomega_(0))=(V_(m))/( sqrt(R^(2)+(eta omega_(0)L-(1)/( eta omega_(0)C))^(2)))`
`=(V_(m))/( sqrt(R^(2)+(eta-(l)/( eta))^(2) (L)/(C)))=(V_(m))/sqrt(1+(Q^(2)+(l)/(4))(eta-(1)/(eta))^(2)(L)/(C))`