In the circuit shown below, the resistance $$R=\sqrt3\times10^3\ \Omega$$, the inductance $$L=2\ \text{H}$$ and the capacitance $$C=1\ \mu\text{F}$$ have been connected to an AC supply of peak voltage $$V_{\max}=5\ \text{V}$$ at a frequency $$\omega$$. Either switch $$S_1$$ or switch $$S_2$$ is closed at a time. In either case, the same maximum current $$i_{\max}$$ is recorded in the circuit. The frequency of the AC source is nearly