Capacitor PYQs - Last 10 Years

If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb an be expressed as :

An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle '\(\alpha\)' with the plates. It leaves the plates at angle '\(\beta\)' with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be ...

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

A capacitor is connected to a 20 V battery through a resistance of 10\(\Omega\). It is found that the potential difference across the capacitor rises to 2 V in 1 \(\mu\)s. The capacitance of the capacitor is __________ \(\mu\)F. Given : $$\...

The circuit shown in the figure consists of a charged capacitor of capacity 3 \(\mu\)F and a charge of \(\mu\)C. At time t = 0, when the key is closed, the value of current flowing through the 5 M\(\Omega\) resistor is 'x' \(\mu\)-A. The va...

A parallel plate capacitor has plate area 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.The ...

Four identical rectangular plates with length, l = 2 cm and breadth, b = \({3 \over 2}\) cm are arranged as shown in figure. The equivalent capacitance between A and C is \({{x{\varepsilon _0}} \over d}\). The value of x is ______________. ...

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, ...

A 2\(\mu\)F capacitor C1 is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C2 of 8 \(\mu\)F. The charge in C2 on equilibrium condition is ...

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \({3 \over 4}\)d, wher...

In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig.) the capacitance...

Effective capacitance of parallel combination
of two capacitors C1 and C2 is 10 μF. When
these capacitors are individually connected to
a voltage source of 1V, the energy stored in the
capacitor C2 is 4 times that of C1. If these
capacitors...

A capacitor is made of two square plates each
of side 'a' making a very small angle \(\alpha\) between
them, as shown in figure. The capacitance will
be close to :

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + \(\alpha\)x) where 'x' is the distance measured from one of...

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and
is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost
in this process by the time the charge is r...

For the given input voltage waveform Vin(t), the output voltage waveform V0(t), across the
capacitor is correctly depicted by :

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....

In the circuit shown, charge on the 5 \(\mu\)F
capacitor is :

A parallel plate capacitor has plate of length
'l', width ‘w’ and separation of plates is ‘d’. It
is connected to a battery of emf V. A dielectric
slab of the same thickness ‘d’ and of dielectric
constant k = 4 is being inserted between the...

A capacitor C is fully charged with voltage V0. After disconnecting the voltage source, it is connected
in parallel with another uncharged capacitor of capacitance \({C \over 2}\). The energy loss in the process
after the charge is distribu...

In the circuit shown in the figure, the total charge is 750 \(\mu\)C and the voltage across capacitor C2
is
20 V. Then the charge on capacitor C2
is :

A 5 \(\mu\)F capacitor is charged fully by a 220 V
supply. It is then disconnected from the supply
and is connected in series to another
uncharged 2.5 \(\mu\)F capacitor. If the energy
change during the charge redistribution is
$${X \over...

A 10 \(\mu\)F capacitor is fully charged to a potential
difference of 50 V. After removing the source
voltage it is connected to an uncharged
capacitor in parallel. Now the potential
difference across them becomes 20 V. The
capacitance of ...

An ideal cell of emf 10 V is connected in circuit
shown in figure. Each resistance is 2 \(\Omega\). The
potential difference (in V) across the capacitor
when it is fully charged is ______.

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

A parallel plate capacitor with square plates is filled with four dielecytrics of dielectrics constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be :

A capacitor with capacitance 5μF is charged to
5μC. If the plates are pulled apart to reduce the
capacitance to 2μF, how much work is done ?

Determine the charge on the capacitor in the
following circuit :

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 capacitors are fully charged, the battery is
removed and after that a dielectric material of
diel...

Voltage rating of a parallel plate capacitor is
500V. Its dielectric can withstand a maximum
electric field of 106 V/m. The plate area is
10–4 m2. What is the dielectric constant is the
capacitance is 15 pF?
(given \(\varepsilon\)0 = 8.86 ...

A parallel plate capacitor has 1μF capacitance.
One of its two plates is given +2μC charge and
the other plate, +4μC charge. The potential
difference developed across the capacitor is:-

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is :

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure :

When is the value of current at t = 4 s ?

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 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :
(Take \(\varepsilon\)0 = 8.85 \(\times\) 10\(-\)12 $...

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 consta...

In the given circuit, the charge on 4 \(\mu\)F capacitor will be :

In the figure shown below, the charge on the left plate of the 10\(\mu\)F capacitor is –30\(\mu\)C. The charge on the right plate of the 6 \(\mu\)F capacitor is :

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

A parallel plate capacitor is of area 6 cm2
and a separation 3 mm. The gap is filled with three dielectric
materials of equal thickness (see figure) with dielectric constants K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a mater...

A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between th...

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

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field
E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :

In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by \(\left( {{C_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)\)

The equivalent capacitance between \(A\) and \(B\) in the circuit given below, is :

A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is \(25 \times {10^{ - 6}}N,\) the value of V is approximately : $...

A capacitor C1 = 1.0 \(\mu\)F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors \({C_2} = 3.0\mu F\) ...

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 = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

A combination of parallel plate capacitors is maintained at a certain potential difference.

When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates i...

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 \(\mu\)C charge, its radius will be :
[ Take : \({1 \over {4\,\pi { \in _0}}} =\) 9 \(\times\) 109 N \(-\) m2/C2 ]