An $L-C-R$ circuit is connected to a source of $A.C.$ current. At resonance,the phase difference between the applied voltage and the current in the circuit is:

$A$ series $LCR$ circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance is increased $(R)$ by $1.4$ times,the resonant frequency now is

In an $L-C-R$ series circuit,the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

Power factor is maximum in an $LCR$ circuit when

In a series resonant $R-L-C$ circuit, the voltage across $R$ is $100 \, V$ and the value of $R = 1000 \, \Omega$. The capacitance of the capacitor is $2 \times 10^{-6} \, F$; the angular frequency of the $AC$ source is $200 \, rad \, s^{-1}$. Then the potential difference across the inductance coil is: (in $V$)