(a) What do you understand by 'sharpness of resonance' for a series LCR resonant circuit? How is it related with the quality factor 'Q' of the circuit? Using the graphs given in the diagram, explain the factors which affect it. For which graph is the resistance (R ) minimum?
(b) `A 2 muF` capacitor, `100 Omega` resistor and 8 H inductor are connected in serieswith an ac source. Find the frequency of the ac source for which the current drawn in the circuit is maximum.
If the peak value of emf of the source is 200 V, calculate the (i) maximum current, and (ii) inductive and capacitive reactance of the circuit at resonance.

Explanation

(a) For graph-A. R is minimum
(b) `v=(1)/(2pisqrt(LC))=(1)/(2xx3.14sqrt(8xx2xx10^(-6)))=318.309`
`I_(0)=(epsilon_(0))/(Z)=(epsilon_(0))/(R)=(200)/(100)=2" AmP "approx318.31" "H_(2)`

`X_(L)=omega_(L)=2pivL=2xxpixx(1000)/(8pi)xx8=2000" "Omega`
`X_(C)=(1)/(omega_(C))=(1)/(2pi ve)=(8pi)/(2pixx1000xx2xx10^(-6))=2000" "Omega`
`"At resonance "X_(L)=X_(C).`