Question

N drops of mercury of equal radii and possessing equal charges combine to form a big drop compare the charge Capacitance and potential of bigger drop withthe corresponding quantities of individual dros

Answer 1

Given: N  drops of mercury of equal radii and possessing equal charges combine to from a big drop.

To find: Compare the charge, capacitance and potential of bigger drop with the corresponding quantities of individual drops.

Solution:

• Let the radius if smaller drop be r and big drop be R, let the charge on smaller drop be q and big drop be Q, potential for small drop be v and big drop be V and the capacitance on smaller drop be c and big drop be C.

• For charge, we have:

            Q = Nq        

            Q / q = N

• Now for capacitance, we have:

• Volume of big drop = N x volume of small drop.

            4/3 x πR³ = N x 4/3 x πr³

            R³ = Nr³

            R/r = ∛N

• Now we have c = 4π∈or

            So c ∝ r

            C / c = R / r = ∛N

• Now for potential, we have:

            v = q / c ..........for small drop

            V = Q / C .........for big drop

• So: v / V = qC / Qc

            v / V = N x 1 / ∛N

            v / V = N^(2/3)

Answer:

The charge, capacitance and potential of bigger drop with smaller drops are:

charge: Q / q = N

capacitance:C / c = ∛N

potential: v / V = N^(2/3)