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Excess Pressure in Bubbles

Two metal sph...

Question

Two metal spheres of capacitance, $C_{1}$ and $C_{2}$ carry some charges. They are put in contact and then separated. The final charges $Q_{1}$ and $Q_{2}$ on them will satisfy:

A

\frac{Q_{1}}{Q_{2}} < \frac{C_{1}}{C_{2}}

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B

\frac{Q_{1}}{Q_{2}} = \frac{C_{1}}{C_{2}}

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C

\frac{Q_{1}}{Q_{2}} > \frac{C_{1}}{C_{2}}

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D

\frac{Q_{1}}{Q_{2}} = \frac{C_{2}}{C_{1}}

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Solution

The correct option is B $\frac{Q_{1}}{Q_{2}} = \frac{C_{1}}{C_{2}}$
Let the charge on two sphere initially are $q_{1} & q_{2}$ . Now when these two capacitors (spheres) are kept in contact with each other and separated. Then charges on the two spheres are,

Let $Q_{1} & Q_{2}$ are the final charges on spheres. So, final charge will be conserved.
$Q_{1} + Q_{2} = q_{1} + q_{2}$

$\frac{Q_{1}}{Q_{2}} = \frac{C_{1} V_{1}}{C_{2} V_{2}}$

The charge will flow until the potential of both the spheres becomes the same.
$\frac{Q_{1}}{Q_{2}} = \frac{C_{1} V}{C_{2} V}$

$\frac{Q_{1}}{Q_{2}} = \frac{C_{1}}{C_{2}}$

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