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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 othervoltage 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. |
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Answer» Solution :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))` |
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