Advertisements
Advertisements
प्रश्न
A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.
Advertisements
उत्तर
Initial capacitance, `C = (∈_0A)/d`
The energy of the capacitor before the insertion of the dielectric is given by `E_1 = 1/2 CV^2 = 1/2 (∈_0A)/d V^2`
After inserting the dielectric slab, the capacitance becomes
`C_1 = KC = K(∈_0A)/d`
and the final voltage becomes
`V_1 = V/K`
Thus, the final energy stored in the capacitor is given by
`E_2 = 1/2 (K∈_0A)/d xx (V/K)^2`
⇒ `E_2 = 1/2 (∈_0AV^2)/(Kd)`
Now ,
Work done = Change in energy
`therefore W = E_2 - E_1`
⇒ `W = 1/2 (∈_0AV^2)/(Kd) - 1/2(∈_0AV^2)/(d)`
⇒ `W = 1/2(∈_0AV^2)/(d)(1/K-1)`
APPEARS IN
संबंधित प्रश्न
As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?
A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the capacitor is
A parallel-plate capacitor has plate area 25⋅0 cm2 and a separation of 2⋅00 mm between the plates. The capacitor is connected to a battery of 12⋅0 V. (a) Find the charge on the capacitor. (b) The plate separation is decreased to 1⋅00 mm. Find the extra charge given by the battery to the positive plate.
Three capacitors having capacitances 20 µF, 30 µF and 40 µF are connected in series with a 12 V battery. Find the charge on each of the capacitors. How much work has been done by the battery in charging the capacitors?
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.
Consider an assembly of three conducting concentric spherical shell of radii a, b and c as shown in figure Find the capacitance of the assembly between the points Aand B.
Suppose the space between the two inner shells is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.
During a thunder storm, the movement of water molecules within the clouds creates friction, partially causing the bottom part of the clouds to become negatively charged. This implies that the bottom of the cloud and the ground act as a parallel plate capacitor. If the electric field between the cloud and ground exceeds the dielectric breakdown of the air (3 × 106 Vm–1), lightning will occur.
- If the bottom part of the cloud is 1000 m above the ground, determine the electric potential difference that exists between the cloud and ground.
- In a typical lightning phenomenon, around 25 C of electrons are transferred from cloud to ground. How much electrostatic potential energy is transferred to the ground?
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
Five capacitor each of capacitance value C are connected as shown in the figure. The ratio of capacitance between P to R, and the capacitance between P and Q is ______.
Two spherical conductors A and B of radii a and b(b > a) are placed concentrically in the air. B is given a charge +Q and A is earthed. The equivalent capacitance of the system is ______.
The radius of a sphere of capacity 1 microfarad in the air is ______
A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε = αU where α = 2V–1. A similar capacitor with no dielectric is charged to U0 = 78V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.
Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is ______.
Two spherical conductors of capacities 4 µF and 3 µF are charged to same potential having radii 4 cm and 3 cm respectively. If ‘σ1’ and ‘σ2’ represent surface density of charge on respective conductors then ______.
What is called the capacity of conductor?
Which units are capacitors commonly measured in practice?
In a series combination, which quantity is the same on each capacitor?
