Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Since the space between the two inner shells is filled with a dielectric, capacitance CAB becomes `C_(AB) = (4pi∈_0abK)/((b-a))` and capacitance CBC becomes `C_(BC) = (4pi∈_0bc)/((c-b))` . Now, as the capacitors are in series, the equivalent capacitance is given by
`1/C = 1/C_(AB) + 1/C_(BC)`
`⇒ C = (C_(AB)C_(BC))/(C_(AB)+C_(BC))`
`⇒ C = (((4pi∈_0)^2 ab^2 Kc)/((b-a)(c-b)))/((4pi∈_0abk)/((b-a))+(4pi∈_0bc)/((c-d)))`
`⇒ C = ((4pi∈_0Kab^2c)/((b-c)(c-b)))/(((abk(c-b)+bc(b-a))/((b-a)(c-b))))`
`⇒ C = (4pi∈_0Kab^2c)/[[abk(c-b)+bc(b-a)]]`
`⇒ C = (4pi∈_0Kabc)/[[ak(c-b)+c(b-a)]]`
APPEARS IN
संबंधित प्रश्न
Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 μF. When the ends X and Y are connected to a 6 V battery, find out (i) the charge and (ii) the energy stored in the network.
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 _________ .
When 1⋅0 × 1012 electrons are transferred from one conductor to another, a potential difference of 10 V appears between the conductors. Calculate the capacitance of the two-conductor system.
Suppose, one wishes to construct a 1⋅0 farad capacitor using circular discs. If the separation between the discs be kept at 1⋅0 mm, what would be the radius of the discs?
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.
Each capacitor shown in figure has a capacitance of 5⋅0 µF. The emf of the battery is 50 V. How much charge will flow through AB if the switch S is closed?
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`
If the voltage applied on a capacitor is increased from V to 2V, choose the correct conclusion.
Calculate the resultant capacitances for each of the following combinations of capacitors.
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 ______.
The capacitance of a parallel plate capacitor is 60 µF. If the distance between the plates is tripled and area doubled then new capacitance will be ______.
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 ______.
The radius of a sphere of capacity 1 microfarad in the air is ______
Can the potential function have a maximum or minimum in free space?
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:
If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then:
- the charge stored in it. increases.
- the energy stored in it, decreases.
- its capacitance increases.
- the ratio of charge to its potential remains the same.
- the product of charge and voltage increases.
Choose the most appropriate answer from the options given below:
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 ______.
