An $AC$ circuit contains a resistance of $1 \text{ k}Omega$,a capacitor of $0.1 \mu\text{F}$,and an inductor of $1 \text{ mH}$ connected in series. The resonance frequency of the circuit is approximately: (in $kHz$)

$A$ series resonant circuit consists of an inductor '$L$' of negligible resistance and a capacitor '$C$' which produces a resonant frequency '$f$'. If '$L$' is changed to $3L$ and '$C$' is changed to $6C$,the new resonant frequency will become:

The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by:

In an electrical circuit,$R$,$L$,$C$,and an $a.c.$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan \frac{\pi}{3} = \sqrt{3})$.

In an $LCR$ series circuit,$C = 2 \mu F$,$L = 1 \ mH$,and $R = 10 \ \Omega$. When the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

$A$ 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).