In an $L-C-R$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

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 a series $LCR$ circuit,at resonance,the peak value of current will be [where $E_0$ is peak emf,$R$ is resistance,$\omega L$ is inductive reactance,and $1/\omega C$ is capacitive reactance].

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

Obtain the resonant frequency $\omega_{r}$ of a series $LCR$ circuit with $L=2.0 \;H, C=32\; \mu F$ and $R=10\; \Omega$. What is the $Q$-value of this circuit?

An $LCR$ series circuit is connected to an external $emf$,$e = 200 \sin(100 \pi t) \ V$. The values of capacitance and resistance in the circuit are $1 \ \mu F$ and $100 \ \Omega$ respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry):