An $LCR$ circuit contains resistance of $110 \, \Omega$ and a supply of $220 \, V$ at $300 \, rad/s$ angular frequency. If only capacitance is removed from the circuit,current lags behind the voltage by $45^{\circ}$. If on the other hand,only inductor is removed,the current leads by $45^{\circ}$ with the applied voltage. The rms current flowing in the circuit will be ...... $A$.

In the given circuit,the peak voltages across $C$,$L$,and $R$ are $30 \,V$,$110 \,V$,and $60 \,V$,respectively. The rms value of the applied voltage is (in $\,V$)

For a series $LCR$ circuit,$R = X_L = 2X_C$. The impedance of the circuit and the phase difference between $V$ and $I$ respectively will be:

For a series $LCR$ circuit,which of the following statements is wrong?

$A$ $750\, Hz$,$20\, V$ (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 $.....s$.

An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $AC$ source of potential difference $V$ volts as shown in the figure. The potential difference across $L$,$C$,and $R$ is $40 \, V$,$10 \, V$,and $40 \, V$,respectively. The amplitude of the current flowing through the $LCR$ series circuit is $10 \sqrt{2} \, A$. The impedance of the circuit is .......... $\Omega$.