Capacitance Questions

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be:

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is:

A fully charged capacitor has a capacitance ‘$C$ ’. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ‘$s$ ’ and mass ‘$m$ ’. If the temperature of the block is raised by ‘$\Delta T$ ’, the potential difference $V$ across the capacitance is:

A parallel plate capacitor is made by stacking $n$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $C$ then the resultant capacitance is:

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is:

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be:

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d$ ($d\ll l$) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity $v$. Then as a function of distance $x$ between them: