Capacitance of Parallel Plate Capacitor

Q.

What is PD and why is it lower than EMF?

Q. An infinite number of identical charges, each $+q\text{coulomb}$, are placed along $\text{x-}$axis at $x=1\text{m},3\text{m},9\text{m},...$ Calculate the electric field at the point $x=0$ due to these charges.

1. $\frac{1}{4\pi {\epsilon }_0}\frac{9q}{10}{\text{NC}}^{-1}$
2. $\frac{1}{4\pi {\epsilon }_0}\frac{9q}{5}{\text{NC}}^{-1}$
3. $\frac{1}{4\pi {\epsilon }_0}\frac{9q}{8}{\text{NC}}^{-1}$
4. $\frac{1}{4\pi {\epsilon }_0}\frac{9q}{7}{\text{NC}}^{-1}$

Q.

The capacitance of the capacitor of plate areas $A_1$ and $A_1$at a distance d, as

shown in the figure, is:

1. 
2. 
3. 
4. 

Q. Separation between plates of a parallel plate capacitor of capacitance $\frac{{ϵ}_{o}A}{d}$ connected to a battery of EMF E is doubled very slowly. Choose the correct option(s).

1. Heat generated in circuit is $\frac{E^2{ϵ}_{o}A}{2d}$
2. Work done by battery when the separation is increasing is $-\frac{E^2{ϵ}_{o}A}{2d}$
3. Work done by electrostatic force is positive during process.
4. Heat generated in circuit is zero.

Q. The force with which the plates of a parallel plate capacitor, having charge Q and area of each plate A, attract each other is

1. zero
2. $\frac{Q^2}{{\epsilon }_{0}A}$
3. $\frac{Q^2}{\sqrt{2}{\epsilon }_{0}A}$
   
4. $\frac{Q^2}{2{\epsilon }_{0}A}$

Q. Three capacitors, each of capacitance $4\mu \text{F}$ are connected to a battery of voltage $10\text{V}$. When key $K$ is closed, the charge which will flow through the battery is

1. $80\mu \text{C}$
2. $40/3\mu \text{C}$
3. $40\mu \text{C}$
4. $20\mu \text{C}$

Q. In the given circuit if each plate surface area is $A$ and plate seperation is $d$. Choose the correct option(s).

1. Equivalent capacitance of system is $\frac{2{ϵ}_{o}A}{d}$
2. Energy stored between plates $1$ and $2$ is $\frac{{ϵ}_{o}A{\text{E}}^2}{2d}$
3. Energy stored between plates $3$ and $4$ is zero
4. Equivalent capacitance of system is $\frac{5{ϵ}_{o}A}{4d}$

Q. Work done by 1 V battery when switch S is closed in $\mu J$is .