Capacitor and Capacitance

When the charge on a capacitor increases keeping geometry the same

A parallel plate capacitor is first charged and then disconnected from the battery and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is

A circuit has a section $AB$, shown in the figure. The emf of the source is equal to $10 \mathrm{V}$ and the capacitance of capacitor are equal to $C_1=1.0 \mathrm{\mu F}$ and $C_2=2.0 \mathrm{\mu F}$. If the potential difference between points $A$ and $B$, ${\varphi }_{\mathrm{A}}-{\varphi }_{\mathrm{B}}=5.0 \mathrm{V},$ then the voltages $V_1$ and $V_2$ across each capacitors, $C_1$ and $C_2$, respectively, are

A capacitor of capacitance $10\mathit{ }\mathrm{\mu F}$ is charged to a potential $50 \mathrm{V}$ with a battery. The battery is now disconnected and an additional charge $200 \mathrm{\mu C}$ is given to the positive plate of the capacitor. The potential difference across the capacitor will be

Two uncharged capacitors are charged with a battery of $E \mathrm{volt}$. The ratio of charges produced on these capacitors $\left(\frac{Q_1}{Q_2}\right)$ will be

The equivalent capacitance of three capacitors of capacitance $C_1,C_2$and $C_3$ are connected in parallel is $12$ units and product $C_1·C_2·C_3=48 \mathrm{units}$. When the capacitors $C_1$and $C_2$ are connected in parallel, the equivalent capacitance is $6 \mathrm{units}$. Then the capacitances are

Which one is the SI unit of capacitance?

An air capacitor of capacity $C=10 \mu \mathrm{F}$ is connected to a constant voltage battery of $12 \mathrm{V}$. Now the space between the plates is filled with a liquid of dielectric constant $5.$ The additional charge that flows now, from the battery to the capacitor is:

Calculate the energy stored in a sphere of radius $4 \mathrm{cm}$ if it is charged to $300 \mathrm{volt}$.

Find the potential difference between these two plates.

Two spherical conductors $A$ and $B$ of radii $a$ and $b\left(b>a\right)$  are placed concentrically in air, The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is :-

A parallel plate capacitor consists of two square plates, each edge $a$. There is a dielectric slab of dielectric constant $K$ in the shape of a cylinder of parabolic cross-section between the plates. The figure shows the cross-section parallel to an edge of the plate.The capacitance of the capacitor $\left(\text{is} \frac{P}{100} \mathrm{fF}\right)$, find $P$.

$\left(\mathrm{Take} K=2, \mathrm{a}=1 \mathrm{mm}\right). \mathrm{Given}{\int }_0^{\mathrm{a}/2}\frac{dx}{\frac{\mathrm{a}}{2}-\frac{{\mathrm{x}}^2}{\mathrm{a}}}=1.2465$

The quantity $X=\frac{{\epsilon }_{0}LV}{t} : {\epsilon }_0$ is the permittivity of free space, $L$ is length, $V$ is potential difference and $t$ is time. The dimensions of $X$ are same as that of :-

A parallel plate air capacitor has a capacitance $C$. When it is half filled with a dielectric of dielectric constant $5$. The percentage increase in the capacitance will be :-

A circuit has a section $AB$, shown in the figure. The emf of the source is equal to $10 \mathrm{V}$ and the capacitors capacitance are equal to $C_1=1.0 \mathrm{\mu F}$ and $C_2=2.0 \mathrm{\mu F}$. If the potential difference between points $A$ and $B$, ${\varphi }_{\mathrm{A}}-{\varphi }_{\mathrm{B}}=5.0 \mathrm{V},$ then the voltages $V_1$ and $V_2$ across each capacitors, $C_1$ and $C_2$, respectively, are

A thin metal plate $\mathrm{P}$ is inserted between the plates of a parallel-plate capacitor of capacitance $\mathrm{C}$ in such a way that its edges touch the two plates. The capacitance now becomes

The radii of two spherical conductors are in ratio $1:2$. The ratio of their capacitance is.

Calculate the capacitance of a spherical conductor of radius $R_1$. It has an adjacent concentric layer of dielectric of permittivity $K$ and outside radius $R_2$. The system is isolated.$\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$

A parallel plate capacitor, a spherical capacitor and cylindrical capacitor is charged by identical battery and then battery is removed from the each capacitor. Consider the following situations

(i) separation between the plates of parallel plate capacitor is reduced

(ii) radius of the outer spherical shell of the spherical capacitor is increased

(iii) radius of the outer cylinder of cylindrical capacitor is increased Which of the following is correct ?

Two charged capacitors with their outer plates fixed and inner plates connected by a spring of force constant $k$ have a charge of $q$ on them. Find the extension in the spring at equilibrium.