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In a series LCR circuit connected to an ac source of variable frequency and voltage v =v_(m)sin omega t,draw a plot showing the variation of current (I) with angularfrequency (omega) for two different values of resistance R_(1) and R_(2) (R_(1) gt R_(2)). Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced ? Define Q-factor of the circuit and give its significance. |
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Answer» Solution : Figure shows the VARIATION of `i_(m)` with`OMEGA` in LCK series circuit for two values of resistance `R_(1) and R_(2) (R_(1) gt R_(2)).` The condition for resonance in the LCR circuit is, `omega_(0)=(1)/(sqrt(LC))` We see that the current amplitude is maximum at the resonantfrequency `omega`. Since `i_(m) =V_(m)//R` at resonance, the current amplitude for case `R_(2)` is sharper to that for case `R_(1)`.  QUALITY factor or simply the Q-factor of a resonantLCR circuit is defined as the ratio of voltage drop across the capacitorto that of applied voltage . It is given by`Q=(1)/(R) sqrt((L)/(C)).` The Q factor determines the sharpness of the resonance curve and if the resonance is less sharp, not only is the maximum current less, the circuit is close to the resonance for a larger range `Delta`w of frequencies and the turning of the circuit will not be GOOD. So, less sharp theresonance, less is the selectivity of the circuit while higher is the Q, sharper is the resonance curve and lesser will be the loss in energy of the circuit. |
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