Lightbulbs A$,$B$,$ and C are connected in the circuit shown above. $($a$)$ List the bulbs in order of their brightness, from brightest to least bright. If any bulbs have the same brightness, state which ones. Justify your answer. Now a switch S and a $5\mathrm{.}0$mH inductor are added to the circuit, as shown above. The switch is closed at time t$=0.($b$)$ Determine the currents IA$,$IB$,$ and IC$$ for the following times. i$.$ Immediately after the switch is closed ii$.$ A long time after the switch is closed $($c$)$ On the axes below, sketch the magnitude of the potential difference VL$$ across the inductor as a function of time, from immediately after the switch is closed until a long time after the switch is closed. $($d$)$ Now consider a similar circuit with an uncharged $5\mathrm{.}0$F capacitor instead of the inductor, as shown above. The switch is again closed at time t$=0.$ On the axes below, sketch the magnitude of the potential difference Vcap$$ across the capacitor as a function of time, from immediately after the switch is closed until a long time after the switch is closed.