Two condensers of capacity $0.3\,\mu F$ and $0.6\,\mu F$ respectively are connected in series. The combination is connected across a potential of $6\,volts$. The ratio of energies stored by the condensers will be
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$(b)$ In series combination $Q$ is constant, hence according to
$U = \frac{{{Q^2}}}{{2C}}$ $==>$ $U \propto \frac{1}{C}$ $==>$ $\frac{{{U_1}}}{{{U_2}}} = \frac{{{C_2}}}{{{C_1}}} = \frac{{0.6}}{{0.3}} = \frac{2}{1}$
$U = \frac{{{Q^2}}}{{2C}}$ $==>$ $U \propto \frac{1}{C}$ $==>$ $\frac{{{U_1}}}{{{U_2}}} = \frac{{{C_2}}}{{{C_1}}} = \frac{{0.6}}{{0.3}} = \frac{2}{1}$
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