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  4. Two capacitors of capacitance C1 and C2, are connected in parallel. If a charge Q is given to the combination, the charge gets shared. The ratio of the charge on the capacitor C1 to the charge on the capacitor C2 is

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Q. Two capacitors of capacitance $C_1$ and $C_2$, are connected in parallel. If a charge Q is given to the combination, the charge gets shared. The ratio of the charge on the capacitor $C_1$ to the charge on the capacitor $C_2$ is

Gujarat CETGujarat CET 2006Electrostatic Potential and Capacitance

Solution:

In parallel combination, they will have common potential.
Common potential $\frac{total \, charge}{total \, capacitance} $
$\therefore V = \frac{Q}{C_1 + C_2}$
$$Charge on $ C_1 = C_1 V = \frac{C_1 Q}{C_1 + C_2}$
$$Charge on $ C_2 = C_2 V = \frac{C_2 Q}{C_1 + C_2}$
$\therefore \, \, \, \, \, $Required ratio = $\frac{C_1 Q / (C_1 + C_2)}{C_2 Q / (C_1 + C_2)}$
$ = \frac{C_1}{C_2}$