Two parallel plate capacitors with different distances between the plates are connected in parallel to a voltage source. A point positive charge $Q$ is moved from a point $1$ that is exactly in the middle between the plates of a capacitor $C_1$ to a point $2$ (which lie in capacitor $C_2$) that lies at a distance from the negative plate of $C_2$equal to half the distance between the plates of $C_1$. Is any work done in the process? If yes, calculate the work done by the field if potential at $1 \mathrm{and} 2$are$V_1$ and $V_2$. 

The lower plate of a parallel plate capacitor is supported on a rigid rod. The upper plate is suspended from one end of a balance. The two plates are joined together by a thin wire and subsequently disconnected. The balance is then counterpoised. Now a voltage $V=5000$ volt is applied between the plates. The distance between the plates is $d=5 \mathrm{mm}$ and the area of each plate is $A=100 {\mathrm{cm}}^2.$ Then find out the additional mass placed to maintain balance. [All the elements other than plates are massless and nonconducting]  

Each plate of a parallel plate air capacitor has an area $S$. What amount of work has to be performed by external agent to slowly increase the distance between the plates from $x_1 \mathrm{to} x_2$ if: 

$\left(\mathrm{i}\right)$ the charge of the capacitor, which is equal to $q$ is kept constant in the process.

$\left(\mathrm{ii}\right)$ the voltage across the capacitor, which is equal to $V$ is kept constant in the process.

Three uncharged capacitors of capacitance $C_1 =1 \mathrm{\mu F}, C_2=2 \mathrm{\mu F}$ and $C_3=3 \mathrm{\mu F}$ are connected as shown in the figure. The potential of point $A, B$ and $D$ are $10 \mathrm{volt}, 25 \mathrm{volt}$ and $20 \mathrm{volt}$ respectively. Determine the potential at point $O$.

Find the potential difference between the points $A$ and $B$ $(V_{\mathit{A}}– V_{\mathit{B}} )$ as shown in the figure. (Initially, all the capacitors are uncharged) 

In a circuit shown in the figure, find the potential difference between the left and right plates of each capacitor.

Find out the charges on the three capacitors connected to a battery as shown in figure. Take $C_1= 1.0 \mathrm{\mu F}, C_2 = 2.0 \mathrm{\mu F}, C_3 = 3.0 \mathrm{\mu F} \mathrm{and} V = 20 \mathrm{volt}.$

$\left(\mathrm{i}\right)$Find out the work done by the battery during the process of charging (initially all the capacitors are uncharged)

$\left(\mathrm{iii}\right)$ Find out the total energy stored in the capacitors.

If you have several $2.0\mathrm{\mu F}$ capacitors, each capable of withstanding $200 \mathrm{volts}$ without breakdown, how would you assemble a combination having minimum number of capacitors and of given equivalent capacitance which capable of withstanding $1000 \mathrm{volts} ;$

$\left(\mathrm{i}\right) 0.40\mathrm{\mu F}$

$\left(\mathrm{b}\right) 1.2\mathrm{\mu F}$

Find the capacitance between the point $\mathrm{A} \mathrm{and} \mathrm{B}$ of the given assemblies.

(a)