Question

A spherical drop of mercury of radius R has a Capacitance given by C = 4πϵ0 R. If two such drops combine to form a single larger drop, what is its capacitance?A spherical drop of mercury of radius R has a Capacitance given by C = 4πϵ0 R. If two such drops combine to form a single larger drop, what is its capacitance?

Answer 1

The capacitance will be

1.26 C

Explanation:

• As the capacitance of a conducting sphere of radius R is C = 4πϵ0 R;
• It is proportional to the radius of the circle
• When two droplets are combined, the volume of the new droplet is twice
• As the volume is proportional to the radius cubed, so the radius of the combined droplet is (2)1/3 = 1.26
• 1.26 times of the smaller droplets and capacitance increases the same way