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Solve Q no.5

5. (a)State the condition for resonance to occur in series LCR a.c. circuit and derive an expression for

resonant frequency. Mention the factors on which the resonant frequency of a series LCR circuit

depends. Plot a graph showing variation of impedance Of series LCR with frequency of an ac source.(b)

Draw a plot showing the variation of the peak current with frequency of the a.c. source used. Define

quality factor Q of the circuitâ€‹

$theconditionfortheresonanceinseriesLCRaccircuitis\phantom{\rule{0ex}{0ex}}Xl=Xc\phantom{\rule{0ex}{0ex}}\omega L=\frac{1}{\omega C}\phantom{\rule{0ex}{0ex}}f=\frac{1}{2\mathrm{\pi}\sqrt{\mathrm{LC}}}theresosnantfrequencyofdependsupontheinduc\mathrm{tan}ceandthecapaci\mathrm{tan}ceonly.\phantom{\rule{0ex}{0ex}}itdoenotdependuponthevalueoftheresis\mathrm{tan}ce\phantom{\rule{0ex}{0ex}}$

The quality factor is the measure of "selectivity" of an AC resonant circuit. Resonant circuits are used to respond selectively to signals of a given frequency while discriminating against signals of different frequencies.

Regards

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