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
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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
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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.
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.