Question

27 spherical drops of radius 3mm and carrying 10^-12 coloumb of charge are combined to form a single drop find the capacitance and potential of bigger drop

Answer 1

it is given that 27 spherical drops each of radius 3 mm are carrying 10^-12 C of charge are combined to form a single drop.

volume of 27 smaller drops = volume of bigger drop

or, 27 × 4/3 πr³ = 4/3 πR³

or, 27r³ = (3r)³ = R³

or, R = 3r

so, capacitance of bigger drop =$4\pi\epsilon_0R$

= $4\pi\epsilon_0(3r)$

=$12\pi\epsilon_0r$

where , $\epsilon_0$= 8.85 × 10^-12 C²/Nm², r = 3mm = 3 × 10^-3 m

so, capacitance of bigger drop , C = 12 × 3.14 × 8.85 × 10^-12 × 3 × 10^-3

= 1000.4 × 10^-15 F

= 1.0004 × 10^-12 F

net charge on bigger drop = 27 × 10^-12

= 27 × 10^-12 C

so, potential of the bigger drop , V = Q/C

= 27 × 10^-12/10^-12 = 27 volts.

Answer 2

Answer:

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Explanation:

it is given that 27 spherical drops each of radius 3 mm are carrying 10^-12 C of charge are combined to form a single drop.

volume of 27 smaller drops = volume of bigger drop

or, 27 × 4/3 πr³ = 4/3 πR³

or, 27r³ = (3r)³ = R³

or, R = 3r

so, capacitance of bigger drop =

where , = 8.85 × 10^-12 C²/Nm², r = 3mm = 3 × 10^-3 m

so, capacitance of bigger drop , C = 12 × 3.14 × 8.85 × 10^-12 × 3 × 10^-3

= 1000.4 × 10^-15 F

= 1.0004 × 10^-12 F

net charge on bigger drop = 27 × 10^-12

= 27 × 10^-12 C

so, potential of the bigger drop , V = Q/C

= 27 × 10^-12/10^-12 = 27 volts.