An ideal resistance $R$,ideal inductance $L$,ideal capacitance $C$,and $AC$ voltmeters $V_{1}, V_{2}, V_{3}$ and $V_{4}$ are connected to an $AC$ source as shown in the figure. At resonance,

An $LCR$ series circuit of capacitance $62.5 \, nF$ and resistance of $50 \, \Omega$ is connected to an $A.C.$ source of frequency $2.0 \, kHz$. For the maximum value of the amplitude of current in the circuit,the value of inductance is $.......... \, mH$. (take $\pi^2 = 10$)

An inductor of inductance $2\,\mu\text{H}$ is connected in series with a resistance,a variable capacitor,and an $AC$ source of frequency $7\,\text{kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}\text{ F}$,where the value of $x$ is $.........$. (Take $\pi = \frac{22}{7}$)

Figure $(a)$ shows the plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ oscillator circuit. Figure $(b)$ shows the phase angle $\phi$ (phase difference between voltage and current) vs $\omega/\omega_0$ graph for the same circuit,for three different quality factors corresponding to graphs $1, 2, 3$ of figure $(a)$. Each graph in figure $(a)$ can be matched by one of the graphs $a, b, c$ in figure $(b)$. Choose the correct statement:

$A$ sinusoidal voltage having a maximum value of $283 \ V$ and a frequency of $50 \ Hz$ is applied to an $LCR$ series circuit where $R = 3 \ \Omega$,$L = 25.48 \ mH$,and $C = 796 \ \mu F$. What is the impedance at resonance condition (in $\Omega$)?

An $AC$ voltage $V = 220 \sin(2 \times 10^3 t) \text{ V}$ is applied to a series $LCR$ circuit. The current amplitude in this circuit is: (Given: $L = 10 \text{ mH}$, $C = 25 \mu\text{F}$, $R = 100 \Omega$) (in $\text{ A}$)