$A$ resistor of $100 \text{ } \Omega$, an inductor of self-inductance $(4/\pi^2) \text{ H}$, and a capacitor of unknown capacity are connected in series to an a.c. source of $200 \text{ V}$ and $50 \text{ Hz}$. When the current and voltage are in phase, the value of the capacity is: (in $\text{ } \mu\text{F}$)

$A$ telegraph line of length $100 \, km$ has a capacity of $0.01 \, \mu F/km$ and it carries an alternating current at $0.5 \, kHz$. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is . . . . . . $mH$. (Take $\pi = \sqrt{10}$)

$A$ series $AC$ circuit consists of an inductor and a capacitor. The inductance and capacitance are $1 \ H$ and $25 \ \mu F$ respectively. If the current is maximum in the circuit,then the angular frequency will be:

For better tuning of a series $LCR$ circuit in a communication system,the preferred combination is

In a radio tuning $RLC$ circuit,the half-power frequencies are $100 \, MHz$ and $120 \, MHz$. Find the quality factor.

$A$ parallel combination of a pure inductor and a capacitor is connected across a source of alternating e.m.f. '$e$'. The currents flowing through the inductor and the capacitor are $i_{L}$ and $i_{C}$ respectively. In this parallel resonant circuit,the condition for the currents $i$,$i_{L}$,and $i_{C}$ is ($i =$ net r.m.s. current in the circuit).