$A$ $750\, Hz$,$20\, V$ (rms) source is connected to a resistance of $100\, \Omega$,an inductance of $0.1803\, H$,and a capacitance of $10\, \mu F$,all in series. The time in which the resistance (heat capacity $2\, J/^{\circ}C$) will get heated by $10^{\circ}C$ (assume no loss of heat to the surroundings) is close to $.....s$.

$A$ sinusoidal voltage of peak value $283 \;V$ and frequency $50 \;Hz$ is applied to a series $LCR$ circuit in which $R = 3 \;\Omega, L = 25.48 \;mH,$ and $C = 796 \;\mu F.$ Find
$(a)$ the impedance of the circuit;
$(b)$ the phase difference between the voltage across the source and the current;
$(c)$ the power dissipated in the circuit; and
$(d)$ the power factor.

In the given circuit,the $AC$ source has $\omega = 100 \ rad/s$. Considering the inductor and capacitor to be ideal,the correct choice$(s)$ is(are):
$(A)$ The current through the circuit,$I$ is $0.3 \ A$
$(B)$ The current through the circuit,$I$ is $0.3 \sqrt{2} \ A$
$(C)$ The voltage across $100 \ \Omega$ resistor $= 10 \sqrt{2} \ V$
$(D)$ The voltage across $50 \ \Omega$ resistor $= 10 \sqrt{2} \ V$

In the $RLC$ series circuit as shown in the diagram,the maximum value of charge on the capacitor is:

$A$ $50 \,W$ 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 ...........

In a circuit,$L$,$C$,and $R$ are connected in series with an alternating voltage source of frequency $f$. When the current in the circuit leads the voltage by $45^{\circ}$,the value of $C$ is