Advertisements
Advertisements
प्रश्न
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
Advertisements
उत्तर
Initially charge on either capacitor is QA = QB = CV
After dielectric is introduced, new capacitance of either capacitor = KC
After opening switch potential across capacitor A is V volts.
Let potential across capacitor B be V1
Therefore QB = CV = C1V1 = KCV1
`"V"_1 = "V"/"K"`
Initial energy in both capacitors = `"CV"^2/2 + "CV"^2/2 = "CV"^2`
Final energy of capacitor A = `"KCV"^2/2`
Final energy of capacitor B = `"KCV"^2/"2K"^2 = "CV"^2/"2K"`
Total final energy of both capacitors = `"KCV"^2/2 + "CV"^2/"2K" = (("K"^2 + 1)/"2K") "CV"^2`
Ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric = `"CV"^2/((("K"^2 + 1)/"2K") "CV"^2) = "2K"/("K"^2 + 1)`
संबंधित प्रश्न
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by
C = `(4piin_0"r"_1"r"_2)/("r"_1 - "r"_2)`
where r1 and r2 are the radii of outer and inner spheres, respectively.
(i) Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.
(ii) If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network?
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?
Three capacitors 2µF, 3µF, and 6µF are joined in series with each other. The equivalent capacitance is ____________.
Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system ______.
Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.
Read the following paragraph and answer the questions.
| A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain the desired value of capacitance. |
- Find the equivalent capacitance between points A and B in the given diagram.
- A dielectric slab is inserted between the plates of the parallel plate capacitor. The electric field between the plates decreases. Explain.
- A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.
OR
Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation d as shown in the figure. Find an expression for the capacitance of the system.
Which units are capacitors commonly measured in practice?
For a given capacitor, what fixes its capacitance?
What is the practical purpose of a series combination of capacitors?
