Three alternating voltage sources $V_1 = 3 \sin \omega t \text{ V}$,$V_2 = 5 \sin(\omega t + \phi_1) \text{ V}$,and $V_3 = 5 \sin(\omega t - \phi_2) \text{ V}$ are connected in series with a resistor $R = \sqrt{\frac{7}{3}} \, \Omega$ as shown in the figure (where $\phi_1 = 30^\circ$ and $\phi_2 = 127^\circ$). Find the peak current (in Ampere) through the resistor.

In the circuit shown in the figure,the $ac$ source gives a voltage $V = 20\cos(2000t)$. Neglecting source resistance,the voltmeter and ammeter readings will be:

Given below are two statements:
Statement $I$: An $AC$ circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement $II$: An $AC$ circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of the above statements,choose the correct answer from the options given below:

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?

With which of the following is the relationship between the phase of current and voltage in an $AC$ circuit represented?

$A$ resistor $R=300 \Omega$ and a capacitor $C=25 \mu F$ are connected in series with a $50 \ V, \frac{50}{\pi} \ Hz$ $AC$ source. The average power dissipated in the circuit is (in $W$)