Advertisements
Advertisements
प्रश्न
A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Advertisements
उत्तर
Radius of the inner sphere, r2 = 12 cm = 0.12 m
Radius of the outer sphere, r1 = 13 cm = 0.13 m
Charge on the inner sphere, q = 2.5 µC = `2.5 xx 10^-6 "C"`
Dielectric constant of a liquid, ` in_"r" = 32`
(a) Capacitance of the capacitor is given by the relation
C = `(4piin_0in_1"r"_1"r"_2)/("r"_1 - "r"_2)`
Where,
`in_0` = Permittivity of free space = `8.85 xx 10^-12 "C"^2 "N"^-1 "m"^-2`
`1/(4piin_0) = 9 xx 10^9 "Nm"^2 "C"^-2`
∴ C = `(32 xx 0.12 xx 0.13)/(9 xx 10^9 xx (0.13 - 0.12))`
`≈ 5.5 xx 10^-9 "F"`
Hence, the capacitance of the capacitor is approximate `5.5 xx 10^-9 "F"`.
(b) Potential of the inner sphere is given by,
`"V" = "q"/"C"`
= `(2.5 xx 10^-6)/(5.5 xx 10^-9) = 4.5 xx 10^2 "V"`
Hence, the potential of the inner sphere is `4.5 xx 10^2 "V"`.
(c) Radius of an isolated sphere, r = 12 × 10−2 m
Capacitance of the sphere is given by the relation,
`"C'" = 4piin_0"r"`
= `4pi xx 8.85 xx 10^-12 xx 12 xx 10^-12`
= `1.33 xx 10^-11 "F"`
The capacitance of the isolated sphere is less in comparison to the concentric spheres. This is because the outer sphere of the concentric spheres is earthed. Hence, the potential difference is less and the capacitance is more than the isolated sphere.
APPEARS IN
संबंधित प्रश्न
When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions
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.
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?
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.
Convince yourself that parts (a), (b) and (c) figure are identical. Find the capacitance between the points A and B of the assembly.
Consider the situation shown in the figure. The switch S is open for a long time and then closed. (a) Find the charge flown through the battery when the switch S is closed. (b) Find the work done by the battery.(c) Find the change in energy stored in the capacitors.(d) Find the heat developed in the system.
A 5⋅0 µF capacitor is charged to 12 V. The positive plate of this capacitor is now connected to the negative terminal of a 12 V battery and vice versa. Calculate the heat developed in the connecting wires.
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.
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.
If the voltage applied on a capacitor is increased from V to 2V, choose the correct conclusion.
A parallel plate capacitor stores a charge Q at a voltage V. Suppose the area of the parallel plate capacitor and the distance between the plates are each doubled then which is the quantity that will change?
Obtain the expression for capacitance for a parallel plate capacitor.
Obtain the expression for energy stored in the parallel plate capacitor.
Dielectric constant for a metal 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 ______.
Can the potential function have a maximum or minimum in free space?
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
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.
