Three capacitors of capacitances $3\,\mu F,\;9\,\mu F$ and $18\,\mu F$ are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases $\left( {\frac{{{C_s}}}{{{C_p}}}} \right)$ will be
Medium
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(a) $\frac{1}{{{C_s}}} = \frac{1}{3} + \frac{1}{9} + \frac{1}{{18}} = \frac{1}{2}$ $==>$ ${C_s} = 2\,\mu F$
${C_p} = 3 + 9 + 18 = 30\mu F$ $==>$ $\frac{{{C_s}}}{{{C_p}}} = \frac{2}{{30}} = \frac{1}{{15}}$
${C_p} = 3 + 9 + 18 = 30\mu F$ $==>$ $\frac{{{C_s}}}{{{C_p}}} = \frac{2}{{30}} = \frac{1}{{15}}$
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$(i)$ The energy stored in the capacitor when the battery is disconnected and the separation is doubled ${E_1}$
$(ii)$ The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is ${E_2}.$
Then ${E_1}/{E_2}$ value is