$500$ Si$.$s$,9\mathrm{.}0$ V The circuit represented above contains a $9\mathrm{.}0$ V battery, a $25$ mF capacitor, a $5\mathrm{.}0$ H inductor, a $5002$ resistor, and a switch with two positions, S$,$ and s$2.$ Initially the capacitor is uncharged and the switch is open. $($a$)$ In experiment $1$ the switch is closed to position S$,$ at time f and left there for a long time. Calculate the value of the charge on the bottom plate of the capacitor a long time after the switch is closed On the axes below, sketch a graph of the magnitude of the charge on the bottom plate of the capacitor as a function of time. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with i$.$ ii$.$ numerical values or algebraic expressions, as appropriate. Time ii$.$ On the axes below, sketch a graph of the current through the resistor as a function of time. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate. Time $($b$)$ In experiment $2$ the capacitor is again uncharged when the switch is closed to position S$,$ at time t$1.$ The switch is then moved to position S$2$ at time $12$ when the magnitude of the charge on the capacitor plate is $105$ mC$,$ allowing electromagnetic oscillations in the LC circuit. i$.$ Calculate the energy stored in the capacitor at time $2.$ i$.$ Calculate the maximum current that will be present during the oscillations. ili. Calculate the time rate of change of the current when the charge on the capacitor plate is $50$ mC