Question

27 identical drops of capacity 10uf combine to form big drop has capacity

Answer 1

Forstly everybody needs to know that potential in each drop is due to the charge stored in it ,distributed evenly acreoss the volume. So,

Let q be the charge stored in each small sphere and Q be the charge in larger aphere formed by all 27 small spheres,so the charge in Q will be 27q.

Thus Q=27q

And v is the volume of each small sphere and V be the volume of larger sphere formed.

Then v=(4/3)*pi*r^3.

Where r is the radius of each small sphere.

Then volume of 27 such spheres will be equql to the volume of larger sphere formed. So,

V=27*(4/3)*pi*r^3………….(1)

Above volume of larger sphere is in terms of radius of smaller spheres(r).

Taking radius of bigger formed sphere be R,volume can be given as,

V=(4/3)*pi*R^3…………..(2)

Comparing eq(1) and eq(2) ,

27*(4/3)*pi*r^3=(4/3)*pi*R^3

Cancelling out terms,

27*r^3=R^3

(3r)^3=R^3

Gives R=3r…………..(3)

Now,potential V’ for small charge is

V’=kq/r=10(given) and

Thus potential V’’ for bigger sphere will be,

V’’=kQ/R=(k*27q)/3r=(27/3)*(kq/r)=9*10

V’’=90volts.

Hence the total potential of the sphere of mercurry formed after combining all 27 spheres,ech of 10 volts potential will be 90volts.

Elaboration@ my beat :)

Hope it helped:)