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JEE Mains | PYQ

A parallel plate capacitor is made up of stair like structure with a plate area \( A \) of each star and that is connected with a wire of length \( b \), as shown in the figure. The capacitance of the arrangement is \( \frac{x}{15} \frac{\varepsilon_{0} A}{b} \). The value of \( x \) is _________.

Two capacitors, each having capacitance \( 40\,\mu \mathrm{F} \) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \( K \) such that the equivalence capacitance of the system became \( 24\,\mu \mathrm{F} \). The value of \( K \) will be:

A parallel plate capacitor is formed by two plates each of area \( 30\pi \, \mathrm{cm^{2}} \) separated by \( 1 \, \mathrm{mm} \). A material of dielectric strength \( 3.6 \times 10^{7} \, \mathrm{V \, m^{-1}} \) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \( 7 \times 10^{-6} \, \mathrm{C} \), the value of dielectric constant of the material is:
[Use \( \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{9} \, \mathrm{N \, m^{2} \, C^{-2}} \) ]

The charge on capacitor of capacitance \( 15\,\mu\text{F} \) in the figure given below is:

Two metallic plates form a parallel plate capacitor. The distance between the plates is \( d \). A metal sheet of thickness \( \frac{d}{2} \) and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

The total charge on the system of capacitors \( C_1 = 1\,\mu F \), \( C_2 = 2\,\mu F \), \( C_3 = 4\,\mu F \) and \( C_4 = 3\,\mu F \) connected in parallel is:
(Assume a battery of \( 20\,\text{V} \) is connected to the combination)

Given below two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A): Non-polar materials do not have any permanent dipole moment.
Reason (R): When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.
In the light of above statements, choose the most appropriate answer from the options given below.

A force of \( 10 \, \text{N} \) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be:

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (\( t_1 \) and \( t_2 \)) as shown in figure. The two different dielectric materials are separated by a conducting foil \( F \). The voltage of the conducting foil is ________ \( \text{V} \).

A parallel plate capacitor with width \( 4 \, \text{cm} \), length \( 8 \, \text{cm} \) and separation between the plates of \( 4 \, \text{mm} \) is connected to a battery of \( 20 \, \text{V} \). A dielectric slab of dielectric constant \( 5 \) having length \( 1 \, \text{cm} \), width \( 4 \, \text{cm} \) and thickness \( 4 \, \text{mm} \) is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ________ \( \varepsilon_{0} \, \text{J} \).
(Where \( \varepsilon_{0} \) is the permittivity of free space).

A parallel plate capacitor with plate area \( A \) and plate separation \( d = 2\,\text{m} \) has a capacitance of \( 4\,\mu\text{F} \). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \( K = 3 \) (as show in figure) will be:

The capacitor of capacitance \( 50 \, \text{pF} \) is charged by \( 100 \, \text{V} \) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is __________ \( \text{nJ} \).

Two parallel plate capacitors of capacity \( C \) and \( 3C \) are connected in parallel combination and charged to a potential difference \( 18 \, \text{V} \). The battery is then disconnected and the space between the plates of the capacitor of capacity \( C \) is completely filled with a material of dielectric constant \( 9 \). The final potential difference across the combination of capacitors will be __________ \( \text{V} \).

A capacitor is discharging through a resistor \( R \). Consider in time \( t_1 \), the energy stored in the capacitor reduces to half its initial value and in time \( t_2 \), the charge stored reduces to one eight of its initial values. The ratio \( t_1 / t_2 \) will be:

Two identical thin metal plates has charge \( q_1 \) and \( q_2 \) respectively such that \( q_1 > q_2 \). The plates were brought close to each other to form a parallel plate capacitor of capacitance \( C \). The potential difference between them is:

Two capacitors having capacitance \( C_1 \) and \( C_2 \) respectively are connected as shown in figure. Initially, capacitor \( C_1 \) is charged to a potential difference \( V \) volt by a battery. The battery is then removed and the charged capacitor \( C_1 \) is now connected to uncharged capacitor \( C_2 \) by closing the switch \( S \). The amount of charge on the capacitor \( C_2 \), after equilibrium, is:

The equivalent capacitance between points \( A \) and \( B \) is below shown figure will be________ \( \mu \text{F} \).

A capacitor of capacitance \( 500\,\mu\text{F} \) is charged completely using a \( dc \) supply of \( 100\,\text{V} \). It is now connected to an inductor of inductance \( 50\,\text{mH} \) to form an \( LC \) circuit. The maximum current in \( LC \) circuit will be ______ \( \text{A} \).

Capacitance of an isolated conducting sphere of radius \( R_1 \) becomes \( n \) times when it is enclosed by a concentric conducting sphere of radius \( R_2 \) connected to earth. The ratio of their radii \( \left( \dfrac{R_2}{R_1} \right) \) is:

A slab of dielectric constant \( K \) has the same cross-sectional area as the plates of a parallel plate capacitor and thickness \( \dfrac{3}{4} d \), where \( d \) is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be:
(Given \( C_{0} = \) capacitance of capacitor with air as medium between plates.)

A parallel plate capacitor filled with a medium of dielectric constant \( 10 \), is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant \( 15 \). Then the energy of capacitor will:

A source of potential difference \( V \) is connected to the combination of two identical capacitors as shown in the figure. When key ‘\( K \)’ is closed, the total energy stored across the combination is \( E_1 \). Now key ‘\( K \)’ is opened and dielectric of dielectric constant \( 5 \) is introduced between the plates of the capacitors. The total energy stored across the combination is now \( E_2 \). The ratio \( {E_1}/{E_2} \) will be: 

A condenser of \( 2 \, \mu \text{F} \) capacitance is charged steadily from \( 0 \) to \( 5 \, \text{C} \). Which of the following graph represents correctly the variation of potential difference (\( V \)) across it’s plates with respect to the charge (\( Q \)) on the condenser?