Idea behind a PPC

Q. A parallel plate capacitor is charged by a battery of emf $\text{V}$. Battery is now disconnected and plates are moved apart slowly to increase the separation to $2d$. Work done by the external agent is

1. $\frac{1}{2}\frac{{\epsilon }_{0}A{V}^2}{d}$
2. $\frac{3}{2}\frac{{\epsilon }_{0}A{V}^2}{d}$
3. $\frac{2{\epsilon }_0{A}^2}{d}$
4. $\frac{5}{2}\frac{{\epsilon }_{0}A{V}^2}{d}$

Q. Twelve capcitors each having a capacitance $C$, are connected to form a cube. Find the equivalent capacitance of the cube along its body diagonal? [Take $C=15\mu \text{F}$]

1. $12\mu \text{F}$
2. $\frac{6}{5}\mu \text{F}$
   
3. $\frac{5}{6}\mu \text{F}$
   
4. $18\mu \text{F}$

Q. There are $n$ identical capacitors which are connected in parallel to a potential difference $V.$ These capacitors are then reconnected in series. The potential difference between the extreme ends is

1. $(n-2)V$
2. $(n-1)V$
3. $0$
4. $nV$

Q. A parallel plate air capacitor with no dielectric between the plates is connected to the constant voltage source. What will be the new capacitance and charge on the capacitor if a dielectric with dielectric constant $K=5$ is inserted between the plates? Intially capacitance and charge on the capacitor are $50\mu \text{F}$ and $200\mu \text{C}$ respectively before the introduction of the dielectric.

1. $50\mu \text{F}$ and $200\mu \text{C}$
2. $50\mu \text{F}$ and $1000\mu \text{C}$
3. $250\mu \text{F}$ and $1000\mu \text{C}$
4. $250\mu \text{F}$ and $200\mu \text{C}$

Q. Capacitance of a parallel plate capacitor is proportional to area of its plates and inversely proportional to distance between the plates.

1. False
2. True

Q. The basic assumption in calculation of capacitance of parallel plate capacitor is that the plates are very large compared to the distance between them.

1. False
2. True

Q. A parallel plate capacitor has a plate area $A$, separation $d$ and charge $Q$. A positive charge $q$ of mass $m$ is released from a point very near to the positive plate. The time taken by the charge to reach to the negative plate of capacitor is
(Neglect gravity)

1. $\sqrt{\frac{4dm{ϵ}_{0}A}{qQ}}$
2. $\sqrt{\frac{3dm{ϵ}_{0}A}{qQ}}$
3. None of these
4. $\sqrt{\frac{2dm{ϵ}_{0}A}{qQ}}$

Q. Some capacitors each of capacitance $30\mu \text{F}$ are connected as shown in the figure. Calculate equivalent capacitance between terminals $\text{A}$ and $\text{B}$ $\left(\text{in}\mu \text{F}\right)$.

Q. Two conductors placed close to each other will have capacitance as compared to its isolated version.

1. more
2. less
3. same

Q. Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries a charge $q$ and the inner shell is neutral. The charge that will flow from inner shell to earth after the switch $S$ is closed is

1. $+\frac{q}{2}$
2. $-\frac{q}{3}$
3. $-\frac{q}{2}$
4. $+\frac{q}{3}$

Q. A parallel plate capacitor has a plate area $A$, separation $d$ and charge $Q$. A positive charge $q$ of mass $m$ is released from a point very near to the positive plate. The time taken by the charge to reach to the negative plate of capacitor is
(Neglect gravity)

1. None of these
2. $\sqrt{\frac{4dm{ϵ}_{0}A}{qQ}}$
3. $\sqrt{\frac{2dm{ϵ}_{0}A}{qQ}}$
4. $\sqrt{\frac{3dm{ϵ}_{0}A}{qQ}}$