Capacitance — JEE Main PYQs

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration …

A capacitor C is fully charged with voltage ${\mathrm{V}}_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{\mathrm{C}}{2}$. The energy loss in the process after the charge is distributed between the two …

Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of $10^6\frac{\mathrm{V}}{\mathrm{m}}$. The plate area is $10^{-4}{\mathrm{m}}^2$. What is the dielectric constant if the capacitance is 15 pF? (given …

A parallel plate capacitor has $1\mu \mathrm{F}$ capacitance. One of its two plates is given $+2\mu \mathrm{C}$ charge and the other plate, $+4\mu \mathrm{C}$ charge. The potential difference developed across the capacitor is:

Determine the charge on the capacitor in the following circuit:

A capacitor with capacitance $5\mu \mathrm{F}$ is charged to $5\mu \mathrm{C}$. If the plates are pulled apart to reduce the capacitance to $2\mu \mathrm{F}$, how much work is done?

A parallel plate capacitor is of area $6{\mathrm{cm}}^2$ and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants ${\mathrm{K}}_1=10$, ${\mathrm{K}}_2=12$ and ${\mathrm{K}}_3=14$. The dielectric c …

Seven capacitors, each of the capacitance $2\mu \mathrm{F}$, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right)\mu \mathrm{F}$. Which of the combinations, shown in figures below, will achieve the desired value?

Two identical parallel plate capacitors, of capacitance C each, have plates of area A , separated by a distance d . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants ${\mathrm{K}}_1,{\mathrm{K}}_2$ …

In the figure shown below, the charge on the left plate of the $10\mu \mathrm{F}$ capacitor is $-30\mu \mathrm{C}$. The charge on the right plate of the $6\mu \mathrm{F}$ capacitor is:

In the given circuit, the charge on $4\mu \mathrm{F}$ capacitor will be :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be $0.5\mu F$. All values in the circuit are in $\mu F$.

A parallel plate capacitor with plates of area $1{\mathrm{m}}^2$ each, are at a separation of 0.1 m . If the electric field between the plates is $100\mathrm{N}/\mathrm{C}$, the magnitude of charge on each plate is:

The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the t …

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants ${\mathrm{K}}_1,{\mathrm{K}}_2,{\mathrm{K}}_3,{\mathrm{K}}_4$ arranged as shown in the figure. The effective dielectric constant K will be:

A parallel plate capacitor is made of two square plates of side ' $a$ ', separated by a distance $\mathrm{d}(\mathrm{d}\ll a$ ). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of to given capacitors. The capacitances are:

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be:

A capacitance of $2\mu \mathrm{F}$ is required in an electrical circuit across a potential difference of 1.0 kV . A large number of $1\mu \mathrm{F}$ capacitors are available which can withstand a potential difference of not more than 300 V .

The minimum number of capacitors …

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4\mu \mathrm{F}$ and $9\mu \mathrm{F}$ capacitors), at a point distant 30 m from it, would e …

In the given circuit, charge ${\mathrm{Q}}_2$ on the $2\mu \mathrm{F}$ capacitor changes as C is varied from $1\mu \mathrm{F}$ to $3\mu \mathrm{F}$. ${\mathrm{Q}}_2$ as a function of 'C' is given properly by: (figures are drawn schematically and are not to scale)

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times 10^4\mathrm{V}/\mathrm{m}$, the charge density of the positive pla …

Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is 'd'. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant ${\mathrm{k}}_1=3$ and thickness …

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 differen …

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