$L, C, R$ represent physical quantities inductance,capacitance,and resistance respectively. The combinations which have the dimensions of frequency are

$A$ resistor of $50 \Omega$,an inductor of self-inductance $(\frac{2}{\pi^2}) \text{ H}$,and a capacitor of unknown capacity are connected in series to an $A$.$C$. source of $100 \text{ V}, 50 \text{ Hz}$. When the voltage and current are in phase,the value of the capacitance is: (in $\mu \text{F}$)

In an $LCR$ series $AC$ circuit at resonance,the value of the power factor will be . . . . . . .

In a series $R-L-C$ $AC$ circuit,for a particular value of $R, L$ and $C$,the power supplied by the source is $P$ at resonance. If the value of inductance is halved,then the power from the source again at resonance is $P'$. Then:

In the circuit shown, the ratio of the quality factor $(Q)$ and the band width $(BW)$ is (Given: band width = $R/L$)

The output voltage (taken across the resistance) of an $L-C-R$ series resonant circuit falls to half its peak value at a frequency of $200 \,Hz$ and again reaches the same value at $800 \,Hz$. The bandwidth of this circuit is ............. $\,Hz$.