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,$L = 1 \mu H$,$C = 1 \mu F$,and $R = 1 k\Omega$. They are connected in series with an $a.c.$ source $V = V_0 \sin \omega t$ as shown. Which of the following options is/are correct?
[$A$] The frequency at which the current will be in phase with the voltage is independent of $R$.
[$B$] At $\omega \sim 0$,the current flowing through the circuit becomes nearly zero.
[$C$] At $\omega \gg 10^6 \text{ rad } s^{-1}$,the circuit behaves like a capacitor.
[$D$] The current will be in phase with the voltage if $\omega = 10^6 \text{ rad } s^{-1}$.

The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be

Find the peak current and resonant frequency of the following circuit (as shown in the figure).

If $L$,$C$,and $R$ are the self-inductance,capacitance,and resistance respectively,which of the following does not have the dimension of time?

$A$ 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 $W$)