In the circuit shown,the readings of voltmeters $V_1, V_2$ and $V_3$ at resonance are given by

An a.c. e.m.f. of peak value $V_0 = 230 \ V$ and frequency $f = 50 \ Hz$ is connected to a circuit with $R = 11.5 \ \Omega$,$L = 2.5 \ H$ and a capacitor $C$ all in series. For the current in the circuit to be maximum,the circuit must be in resonance. Find the value of $C$ and the maximum current $I_{max}$ (take $\pi^2 = 10$).

In a series $R-L-C$ $AC$ circuit,for a particular value of $R, L$ and $C$,the power supplied by the source is $P$ at resonance. If the value of inductance is halved,then the power from the source again at resonance is $P'$. Then:

$A$ transmitting station releases waves of wavelength $960\, m$. $A$ capacitor of $2.56\, \mu F$ is used in the resonant circuit. The self-inductance of the coil necessary for resonance is $............ \times 10^{-8}\, H$.

In an $LCR$ circuit,the inductance is changed from $L$ to $9 L$. For the same resonant frequency,the capacitance should be changed from $C$ to:

$A$ $100 \, \Omega$ resistance,a $0.1 \, \mu \text{F}$ capacitor,and an inductor are connected in series across a $250 \, \text{V}$ supply at variable frequency. Calculate the value of inductance of the inductor at which resonance will occur. Given that the resonant frequency is $60 \, \text{Hz}$. (In $\text{H}$)