MCQ
A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitances : $C_2 = 2C$ and $C_3 \rightarrow \infty$ . Bodies $2 $ and $3 $ are initially uncharged. "Body $2$ is touched with body $1$. Then, body $2$ is removed from body $1 $ and touched with body $3$, and then removed." This process is repeated $N$ times. Then, the charge on body $1$ at the end must be
  • $Q/3^N$
  • B
    $Q/3^{N-1}$
  • C
    $Q/N^3$
  • D
    None

Answer

Correct option: A.
$Q/3^N$
a
When we touched first time charge on first capacitor beacomes $\frac{Q}{3}$ and on second capacitor it becomes $\frac{2 Q}{3}$ But when $2 C$ is touched with $C \rightarrow \infty$ it becomes uncharged so after first operation.

$Q_{1}=\frac{Q}{3}$

after $I I^{n d}$ operation $Q_{2}=\frac{1}{3}\left(\frac{Q}{3}\right)=\frac{Q}{3^{2}}$

so after $N^{t h}$ operation $Q_{N}=\frac{Q}{3^{N}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Assertion : The logic gate $NOT$ can be built using diode.

Reason : The output voltage and the input voltage of the diode have $180^o$ phase difference.

The distance between $\mathrm{H}^{+}$ and $\mathrm{Cl}^{-}$ ions in HCl molecule is 1.28 Å. What will be the potential due to this dipole at a distance of 12 Å on the axis of dipole(a) (b) (c) (d)
The magnetic flux linked with a coil is $\phi\leq8\text{t}^2+3\text{t}+5$ Weber. The induced emf in fourth second will be.
The potential difference between $A$ and $B$ in the Figure is .............. $V$
A long magnet is cut in two parts in such a way that the ratio of their lengths is 2 : 1. The ratio of pole strengths of both the section is
The earth's magnetic field at a certain place has a horizontal component $0.3$ $Gauss$ and the total strength $0.5$ $Gauss$. The angle of dip is
The electric potential in a region is represented as $V = 2x + 3y -z$ ; then the expression of electric field strength is
A plano-convex lens of refractive index $1.5$ and radius of curvature $30 cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object.......$cm$
When objects at different distances are seen by the eye, which of the following remain constant?
A proton beam is going from north to south and an electron beam is going from south to north. Neglecting the earth's magnetic field, the electron beam will deflected (Zero gravity)