Potential and Potential Difference

Q. A parallel-plate capacitor has plates of area $A$ and separation $d$ and is charged to a potential difference $V$. The charging battery is then disconnected and the plates are pulled apart until their separation is $2d$. What is the work required to separate the plates?

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

Q. An uncharged parallel-plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel-plate capacitor charged to a potential $V_0$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is

1. $\frac{V_0}{V}-1$
2. $\frac{V_0}{V}+1$
3. $\frac{V}{V_0}-1$
4. $\frac{V}{V_0}+1$

Q. If $100volts$ of potential difference is applied between a and b in the circuit of given figure. Find the potential difference (in $V$) between c and d.

Q. The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

1. $W$
2. $2W$
3. $4W$
4. $8W$

Q. The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

1. $W$
2. $2W$
3. $4W$
4. $8W$