The $LC$ parallel resonant circuit:

Give the value of impedance in resonance condition.

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

An inductor coil is connected to a capacitor and an $AC$ source of rms voltage $8 \, V$ in series. The rms current in the circuit is $16 \, A$ and is in phase with the emf. If this inductor coil is connected to a $6 \, V$ $DC$ battery, the magnitude of the steady current is (in $A$)

Figure $(a)$ shows a plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ 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 $(b)$. Which of the following statements is correct?

In the circuit shown,the $AC$ source has voltage $V=20 \cos (\omega t) \text{ V}$ with $\omega=2000 \text{ rad/s}$. The magnitude of the amplitude current will be nearly