In an $LCR$ circuit,the capacitance is changed from $C$ to $4C$. For the same resonant frequency,the inductance should be changed from $L$ to:

In an electrical circuit,$R, L, C$ and an $AC$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\pi / 3$. If instead,$C$ is removed from the circuit,the phase difference is again $\pi / 3$. The power factor of the circuit is

The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. For what frequency point is the circuit capacitive?

In a series $RLC$ circuit,the $r.m.s.$ voltages across the resistor and the inductor are respectively $400 \,V$ and $700 \,V$. If the equation for the applied voltage is $\varepsilon = 500 \sqrt{2} \sin \omega t$,then the peak voltage across the capacitor is ........... $V$.

$A$ $220 \; V, 50 \; Hz$ $AC$ source is connected to a $25 \; V, 5 \; W$ lamp and an additional resistance $R$ in series (as shown in the figure) to run the lamp at its rated power. The value of $R$ (in $\Omega$) will be:

$A$ $50 \,W$ bulb connected in series with a heater coil is put to an $AC$ mains. Now the bulb is replaced by a $100 \,W$ bulb. The heater output will ...........