In an $LCR$ series resonant circuit,at resonance,the voltage across $L$ and $C$ will cancel each other because they are:

An $LCR$ circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied. The frequency,at which the voltage across the resistor is maximum,is......$Hz$.

$A$ series resonant circuit consists of an inductor '$L$' of negligible resistance and a capacitor '$C$' which produces a resonant frequency '$f$'. If '$L$' is changed to $3L$ and '$C$' is changed to $6C$,the new resonant frequency will become:

In an a.c. $LCR$ circuit,a capacitor and an inductor in series are connected with an a.c. voltage source of $90\,V$. An ammeter and a voltmeter are connected in the circuit to measure the current in the circuit and the voltage across the capacitor plus the inductor combination. If $X_L = X_C = 4\,\Omega$ and $R = 45\,\Omega$,the readings of the ammeter $(I)$ and the voltmeter $(V)$ are:

$A$ resistor of $100 \Omega$,an inductor of self-inductance $(\frac{4}{\pi^2}) \text{ H}$,and a capacitor of unknown capacitance are connected in series to an $A$.$C$. source of $200 \text{ V}, 50 \text{ Hz}$. When the current and voltage are in phase,the capacitance and the power dissipated are respectively:

$A$ tuned amplifier circuit is used to generate a carrier frequency of $ 2 \text{ MHz} $ for amplitude modulation. The value of $ \sqrt{LC} $ is