In the shown $AC$ circuit,the phase difference between currents $I_1$ and $I_2$ is:

Give the name of the physical quantity in an $LCR$ circuit that corresponds to mass $m$ in forced oscillations.

Answer the following questions:
$(a)$ In any $ac$ circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for $rms$ voltage?
$(b)$ Why is a capacitor used in the primary circuit of an induction coil?
$(c)$ An applied voltage signal consists of a superposition of a $dc$ voltage and an $ac$ voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the $dc$ signal will appear across $C$ and the $ac$ signal across $L$.
$(d)$ $A$ choke coil in series with a lamp is connected to a $dc$ line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp's brightness. Predict the corresponding observations if the connection is to an $ac$ line.
$(e)$ Why is a choke coil needed in the use of fluorescent tubes with $ac$ mains? Why can we not use an ordinary resistor instead of the choke coil?

Mark the incorrect statement.

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit,the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown below. If a student plots graphs of the square of maximum charge $(Q_{Max}^2)$ on the capacitor with time $(t)$ for two different values $L_1$ and $L_2$ $(L_1 > L_2)$ of $L$,then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale.)

In the given $AC$ circuit,when switch $S$ is at position $1$,the source $emf$ leads the current by $\pi / 6$. Now,if the switch is at position $2$,then