In an $LCR$ circuit having $L = 8.0 \, H$,$C = 0.5 \, \mu F$,and $R = 100 \, \Omega$ in series,the resonance frequency in radians per second is:

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:

An $ac$ source of variable frequency $f$ is connected to an $LCR$ series circuit. Which one of the graphs represents the variation of current $I$ in the circuit with frequency $f$?

The reading of the ammeter in the circuit shown will be: (in $A$)

$A$ series $LCR$ circuit is connected to an ac voltage source. When $L$ is removed from the circuit,the phase difference between current and voltage is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is:

$A$ 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 $\text{ } \mu\text{F}$)