If the input voltage $V_i$ to the circuit below is given by $V_i(t) = A \cos (2 \pi f t)$ and the output voltage is given by $V_o(t) = B \cos (2 \pi f t + \phi)$,which one of the following four graphs best depicts the variation of $\phi$ versus $f$?

There is a $100\,\Omega$ resistance in an $L-C-R$ $AC$ circuit. An $AC$ $emf$ of $200\,V$ and $\omega = 300\,rad/s$ is applied to this circuit. When only the capacitor is removed,the current lags the voltage by $60^o$. When only the inductor is removed,the current leads the voltage by $60^o$. The current in this $L-C-R$ circuit will be.....$A$

Mark the incorrect statement.

An inductor stores $16 \ J$ of magnetic field energy and dissipates $32 \ W$ of thermal energy due to its resistance when an $A.C.$ current of $2 \ A$ $(rms)$ and frequency $50 \ Hz$ flows through it. The ratio of inductive reactance to its resistance is . . . . . . . $(\pi=3.14)$

In the circuit shown, the charge $q$ varies with time $t$ as $q = t^2 - 5$, where $q$ is in coulomb and $t$ is in second. At time $t = 3$ second, the voltage $V_{AB}$ in volt will be:

An $AC$ voltage source of $E = 150 \sin(100t)$ is used to run a device which offers a resistance of $20 \,\Omega$ and restricts the flow of current in one direction only. The $r.m.s.$ value of current in the circuit will be.....$A$