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Q)

Three identical capacitors each of capacitance $3 \mu F$ are connected in term in series and in parallel combination to the common source of V volt . find out the ratio of the energies stored in two configurations.

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A)
Solution :
$C_s= \large\frac{1}{3} +\frac{1}{3} +\frac{1}{3}$
$C_p=3+3+3=9$
$\quad= 9 \mu F$
Energy when connected in series is $\large\frac{1}{2} $$C_sv^2$
$E_s= \large\frac{1}{2}$$\times 1 \times v$
Energy when connected in parallel is $\large\frac{1}{2} $$C_pv^2$
$E_p= \large\frac{1}{2} $$ \times 9 \times v$
$\therefore \large\frac{E_s}{E_p}= \frac{1/2 \times 1 \times v}{1/2 \times 9 \times v}$
$\qquad= 1:9$
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