An inductor of inductance $2 \mu H$ is connected in series with a resistance,a variable capacitor and an a.c. source of frequency $5 \text{ kHz}$. 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 $\pi^2 = 10$).

$A$ parallel combination of a pure inductor and a capacitor is connected across a source of alternating e.m.f. '$e$'. The currents flowing through the inductor and the capacitor are $i_{L}$ and $i_{C}$ respectively. In this parallel resonant circuit,the condition for the currents $i$,$i_{L}$,and $i_{C}$ is ($i =$ net r.m.s. current in the circuit).

When resonance is produced in a series $LCR$ circuit,then which of the following is not correct?

Resonance frequency of $L-C-R$ series $AC$ circuit is $f_0$. Now,if the inductance is reduced to $\frac{1}{4}$ times and the capacitance is increased to $16$ times,then the new resonance frequency becomes:

$A$ series $LCR$ circuit contains inductance $5 \ mH$,capacitance $2 \ \mu F$,and resistance $10 \ \Omega$. If the frequency of the $A.C.$ source is varied,what is the frequency at which maximum power is dissipated?

For the series $LCR$ circuit shown in the figure,what is the resonance angular frequency and the amplitude of the current at the resonating frequency? The source voltage is given as $220 \, V$ ($RMS$ value).