Question:
Twenty seven drops of same size are charged at $220\text{ V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.}
Twenty seven drops of same size are charged at $220\text{ V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.}
Show Hint
For $n$ identical droplets combining, the potential of the big drop is always $V_{big} = n^{2/3} \times V_{small}$. Here, $27^{2/3} = (3^3)^{2/3} = 3^2 = 9$.
Updated On: May 15, 2026
- $1320\text{ V}$
- $1520\text{ V}$
- $1980\text{ V}$
- $660\text{ V}$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
When small charged droplets coalesce into a single large drop, two physical quantities remain conserved: Total Volume and Total Charge. The electric potential $V$ of a spherical drop of radius $r$ and charge $q$ is given by:
$$V = \frac{kq}{r}$$
By finding the relationship between the radius and charge of the small drops versus the large drop, we can determine the new potential.
Step 1: Relation between radii using Volume Conservation. Let the radius of each small drop be $r$ and the radius of the big drop be $R$. The volume of 27 small drops equals the volume of 1 big drop: $$27 \times \left( \frac{4}{3}\pi r^3 \right) = \frac{4}{3}\pi R^3$$ $$27r^3 = R^3$$ Taking the cube root on both sides: $$R = 3r$$
Step 2: Relation between charges using Charge Conservation. Let the charge on each small drop be $q$ and the charge on the big drop be $Q$. $$Q = 27q$$
Step 3: Calculating the potential of the bigger drop. Potential of a small drop ($v$): $v = \frac{kq}{r} = 220\text{ V}$. Potential of the big drop ($V$): $$V = \frac{kQ}{R}$$ Substitute $Q = 27q$ and $R = 3r$: $$V = \frac{k(27q)}{3r} = 9 \left( \frac{kq}{r} \right)$$ $$V = 9 \times v$$ $$V = 9 \times 220 = 1980\text{ V}$$
Step 1: Relation between radii using Volume Conservation. Let the radius of each small drop be $r$ and the radius of the big drop be $R$. The volume of 27 small drops equals the volume of 1 big drop: $$27 \times \left( \frac{4}{3}\pi r^3 \right) = \frac{4}{3}\pi R^3$$ $$27r^3 = R^3$$ Taking the cube root on both sides: $$R = 3r$$
Step 2: Relation between charges using Charge Conservation. Let the charge on each small drop be $q$ and the charge on the big drop be $Q$. $$Q = 27q$$
Step 3: Calculating the potential of the bigger drop. Potential of a small drop ($v$): $v = \frac{kq}{r} = 220\text{ V}$. Potential of the big drop ($V$): $$V = \frac{kQ}{R}$$ Substitute $Q = 27q$ and $R = 3r$: $$V = \frac{k(27q)}{3r} = 9 \left( \frac{kq}{r} \right)$$ $$V = 9 \times v$$ $$V = 9 \times 220 = 1980\text{ V}$$
Was this answer helpful?
1
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Electrostatics Questions
- The electric field intensity (\(E\)) at a distance of 3 m from a uniform long straight wire of linear charge density 0.2 \(\mu C m^{-1}\) is:
- The capacitance of an isolated sphere of radius \( r_1 \) is increased by 5 times when enclosed by an earthed concentric sphere of radius \( r_2 \). The ratio \( \frac{r_1}{r_2} \) is:
- Two spheres A & B of radii 4 cm & 6 cm are given charges of 80 µC & 40 µC respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is:
- The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial line is:
Two condensers \( C_1 \) & \( C_2 \) in a circuit are joined as shown in the figure. The potential of point A is \( V_1 \) and that of point B is \( V_2 \). The potential at point D will be:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions