In an $LC$ circuit shown in figure, if the switch is closed at $t=0$, find the equation for instantaneous current in $\mathrm{mA}.Q_{\max }=100\mu \mathrm{C},L=40\mathrm{mH},C=100\mu \mathrm{F}$

If the emf of the $AC$ source in the figure is $\epsilon =10\sqrt{2}\sin 100\pi t$, where $\epsilon$ is in volt and $t$ is in second, then the expression for the current (in ampere) in the circuit is

If the reading of voltmeters $V_1$ and $V_2$ each is $25 \mathrm{V}$ then the reading of voltmeter $V_3$ will be

Assuming source to be ideal the phase difference between currents $I_1$ and $I_2$ is

In the circuit shown, the value of resistance $R$ if the total voltage is in phase with the total current is nearly

The variation of voltage $\left(V\right)$ with time $\left(t\right)$ is shown in the graph. The rms value of voltage is

The average power dissipated in the given circuit is