electrostatic-potential-and-capacitance Question 44

Question: Q. 18. Eight identical spherical drops, each carrying a charge 1nC are at a potential of 900 V each. All these drops combine together to form a single large drop. Calculate the potential of this large drop.

(Assume no wastage of any kind and take the capacitance of a sphere of radius r as proportional to r ).

U] [CBSE SQP 2014]

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Solution:

Ans. Let the radius of each drop be r. The capacitance C of each drop is kr, where k is a constant.

Also q=CV,V=900 volt

Charge on each drop =q=(kr×900)C1/2 Total charge on all the eight drops =Q=8q

=7200kr1/2

Let R be the radius of the large drop. Then

4π3R3=8×4π3r3 R=(8)1/3r=2r

Capacitance C of the large drop =kR=2kr1/2

Potential of the large drop =QC=7200kr2kr volt

=3600 V

[CBSE Marking Scheme 2014]



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