Advertisements
Advertisements
प्रश्न
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure . The width of each stair is a and the height is b. Find the capacitance of the assembly.
Advertisements
उत्तर
The total area of the flat plate is A. The width of each stair is the same. Therefore, the area of the surface of each stair facing the flat plate is the same, that is, `A/3` .
From the figure, it can be observed that the capacitor assembly is made up of three capacitors. The three capacitors are connected in parallel.
For capacitor C1, the area of the plates is `A/3` and the separation between the plates is d.
For capacitor C2, the area of the plates is `A/3` and the separation between the plates is (d + b).
For capacitor C3, the area of the plates is `A/3` and the separation between the plates is (d + 2b).
Therefore ,
`C_1 = (∈_0A)/(3d)`
`C_2 = (∈_0A)/(3(d+b)`
`C_3 = (∈_0A)/(3(d+2b)`
As the three capacitors are in parallel combination,
`C = C_1 + C_2 + C_3`
⇒ `C = (∈_0A)/(3d) + (∈_0A)/(3(d+b)) + (∈_0A)/(3(d+2b)`
⇒ `C = (∈_0A)/3 ((3d^2 + 6bd + 2b^2))/(d(d+b)(d+2b))`
APPEARS IN
संबंधित प्रश्न
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?
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
Two metal spheres of capacitance C1 and C2 carry some charges. They are put in contact and then separated. The final charges Q1 and Q2 on them will satisfy
The plates of a parallel-plate capacitor are made of circular discs of radii 5⋅0 cm each. If the separation between the plates is 1⋅0 mm, what is the capacitance?
Find the charges on the three capacitors connected to a battery as shown in figure.
Take `C_1 = 2.0 uF , C_2 = 4.0 uF , C_3 = 6.0 uF and V` = 12 volts.
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
A parallel-plate capacitor of capacitance 5 µF is connected to a battery of emf 6 V. The separation between the plates is 2 mm. (a) Find the charge on the positive plate. (b) Find the electric field between the plates. (c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination. (d) How much charge has flown through the battery after the slab is inserted?
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.
An air-filled parallel-plate capacitor is to be constructed which can store 12 µC of charge when operated at 1200 V. What can be the minimum plate area of the capacitor? The dielectric strength of air is `3 xx 10^6 "Vm"^-1`
You are provided with 8 μF capacitors. Show with the help of a diagram how you will arrange minimum number of them to get a resultant capacitance of 20 μF.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Capacitors P and Q have identical cross-sectional areas A and separation d. The space between the capacitors is filled with a dielectric of dielectric constant Er as shown in the figure. Calculate the capacitance of capacitors P and Q.
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
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.
Can the potential function have a maximum or minimum in free space?
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 `3/4`d, where 'd' is the separation between the plate of the parallel plate capacitor.
The new capacitance (C') in terms of the original capacitance (C0) is given by the following relation:
A capacitor of capacity 2 µF is charged to a potential difference of 12 V. It is then connected across an inductor of inductance 0.6 mH. The current in the circuit at a time when the potential difference across the capacitor is 6.0 V is ______ × 10-1A.
The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness `3/8 d and d/2`, respectively, are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1 = 1.25 K, the value of K1 is:
