Two circuits are shown in the figures $(a)$ and $(b)$. At a frequency of $....\,rad/s$,the average power dissipated in one cycle will be the same in both circuits.

$A$ series $LCR$ circuit with inductance $L = 10\,H$,capacitance $C = 10\,\mu F$,and resistance $R = 50\,\Omega$ is connected to an $AC$ source of voltage $V = 200 \sin(100t)\,V$. If the resonant frequency of the $LCR$ circuit is $\nu_{0}$ and the frequency of the $AC$ source is $\nu$,then:

$A$ series $LCR$ circuit driven by $300 \, V$ at a frequency of $50 \, Hz$ contains a resistance $R = 3 \, k\Omega$, an inductor of inductive reactance $X_{L} = 250 \pi \, \Omega$ and an unknown capacitor. The value of capacitance to maximize the average power should be: (Take $\pi^{2} = 10$) (in $\mu F$)

Using a variable-frequency a.c. voltage source, the maximum current measured in the given $LCR$ circuit is $50 \text{ mA}$ for $V = 5 \sin(100t)$. The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor $(C)$ used is . . . . . . $\mu\text{F}$.

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?

What is resonance in an $LCR$ series circuit?