Two capacitors, C $1=18\mathrm{.}0$ mF and C $2=36\mathrm{.}0$ mF$,$ are connected in series, and a $12\mathrm{.}0-$V battery is connected across

the two capacitors. Find $($a$)$ the equivalent capacitance and $($b$)$ the energy stored in this equivalent capacitance. $($c$)$ Find

the energy stored in each individual capacitor. $($d$)$ Show that the sum of these two energies is the same as the energy

found in part $($b$).($e$)$ Will this equality always be true, or does it depend on the number of capacitors and their capaci$-$

tances$?($f$)$ If the same capacitors were connected in parallel, what potential difference would be required across them

so that the combination stores the same energy as in part $($a$)?($g$)$ Which capacitor stores more energy in this situation,

C $1$ or C $2?$