The $LC$ series resonant circuit produces a resonant frequency '$f$'. If $L$ is tripled and $C$ is increased by $3C$, the resonant frequency will be

$A$ coil has an inductance of $0.7 \, H$ and is joined in series with a resistance of $220 \, \Omega$. When an alternating $emf$ of $220 \, V$ at $50 \, Hz$ is applied to it,the phase angle by which the current lags behind the applied $emf$ and the wattless component of the current in the circuit are respectively:

An e.m.f. $E = E_0 \cos \omega t$ is applied to an $L-R$ circuit. The inductive reactance is equal to the resistance $R$ of the circuit. The power consumed in the circuit is:

$A$ $400 \Omega$ resistor, a $250 \text{ mH}$ inductor, and a $2.5 \mu \text{F}$ capacitor are connected in series with an $AC$ source of peak voltage $5 \text{ V}$ and angular frequency $\omega = 2000 \text{ rad/s}$. What is the peak value of the electrostatic energy of the capacitor (in $\mu \text{J}$)?

An inductance coil has a resistance of $100 \Omega$. When an $A.C.$ signal of frequency $100 \ Hz$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

For the $AC$ circuit shown below,the phase difference between emf and current is $\frac{\pi}{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \Omega$,then the values of $P$ and $Q$ are