A coil of inductance $L$ has an inductive reactance of ${X_L}$ in an AC circuit in which the effective current is I. The coil is made from a super-conducting material and has no resistance. The rate at which power is dissipated in the coil is

In $LR$ circuit the current increases to one fourth of its maximum value in $4\,sec$, then the time constant of the circuit is

An $ac$ source of angular frequency $\omega$ is fed across a resistor r and a capacitor $C$ in series. The current registered is $I$. If now the frequency of source is changed to $\omega$ $/3$ (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an $ac$ source. ${V_1}$ and ${V_2}$ are voltmeters and $A$ is an ammeterConsider               now the following statements

             $I$.Readings in $A$ and $V_2$ are always in phase

             $II$.Reading in $V_1$ is ahead in phase with reading in $V_2$

             $III$.Readings in $A$ and $V_1$ are always in phase which of these statements are/is correct

A circuit connected to an $ac$ source of $emf$ $e = e_0\, sin\, (1000t)$ with $t$ in seconds, gives a phase difference of $\frac{\pi }{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?