Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.
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?
Three identical capacitors C1, C2 and C3 of capacitance 6 μF each are connected to a 12 V battery as shown.
Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors
The equivalent capacitance of the combination shown in the figure 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
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.
Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure . Find the capacitance.
Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Obtain the expression for capacitance for a parallel plate capacitor.
Obtain the expression for energy stored in the parallel plate capacitor.
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.
Dielectric constant for a metal 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 ______.
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.
A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio of final charges on A and B.
