A spherical drop of capacitance 1,mu F is bro | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the radius of the large drop be $R$ and its capacitance be $C = 4\pi\epsilon_0 R = 1\,\mu F$.Let the radius of each small drop be $r$. Since t

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(C) Let the radius of the large drop be $R$ and its capacitance be $C = 4\pi\epsilon_0 R = 1\,\mu F$.Let the radius of each small drop be $r$. Since the volume remains constant,the volume of the large drop equals the sum of the volumes of the $8$ small drops:$\frac{4}{3}\pi R^3 = 8 	imes \frac{4}{3}\pi r^3$$R^3 = 8r^3 \implies R = 2r$ or $r = R/2$.The capacitance of each small drop is $c = 4\pi\epsilon_0 r$.Substituting $r = R/2$,we get $c = 4\pi\epsilon_0 (R/2) = C/2$.Given $C = 1\,\mu F$,the capacitance of each small drop is $c = 1/2 = 0.5\,\mu F$.

$A$ spherical drop of capacitance $1\,\mu F$ is broken into eight drops of equal radius. Then,the capacitance of each small drop is ......$\mu F$.

Similar Questions

Which one of the following is the correct dimensional formula for the capacitance in $F$? $M, L, T$ and $C$ stand for units of mass,length,time,and charge respectively.

Two isolated conductors are charged by transferring electrons from one to the other. If transferring $6.25 \times 10^{15}$ electrons from one conductor to the other creates a potential difference of $100 \, V$,what is the capacitance of the system in $\mu F$?

The respective radii of the two spheres of a spherical condenser are $12 \; cm$ and $9 \; cm$. The dielectric constant of the medium between them is $6$. The capacity of the condenser will be

Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is $C$,then the capacity of the big drop is: (in $C$)

The dimension of capacitance is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module