Advertisements
Advertisements
प्रश्न
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
पर्याय
1 : 1
1 : 2
2 : 1
1 : 3
Advertisements
उत्तर
1 : 1
Explanation:
The potential energy stored in the capacitor equals the work done in charging the capacitor. The capacitor is charged by working against the existing electric field between the two plates.
Denote the charge stored by the capacitor of capacitance C when it is fully charged as Q. Denote the battery voltage as V.
The potential energy U, stored in the capacitor, can be represented as:
U = `1/2 "CV"^2`
The work done by battery W, in supplying charge Q can be represented as:
W = QV
⇒ W = (CV)V
⇒ W = CV2
Therefore, the energy dissipated during charging H equals the difference between W and U.
H = W – U
H = `"CV"^2 - 1/2 "CV"^2`
H = `1/2 "CV"^2`
The ratio of and is calculated as follows:
`"U"/"H" = (1/2 "CV"^2)/(1/2 "CV"^2)`
`"U"/"H" = 1/1` i.e. 1 : 1
APPEARS IN
संबंधित प्रश्न
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
The energy density in the electric field created by a point charge falls off with the distance from the point charge as
Find the charge on the capacitor shown in the figure.
(a) Find the current in the 20 Ω resistor shown in the figure. (b) If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state?
A 20 μF capacitor is joined to a battery of emf 6.0 V through a resistance of 100 Ω. Find the charge on the capacitor 2.0 ms after the connections are made.
The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10 Ω at t = 0. Find the charge on the capacitor in the circuit at (a) t = 0 (b) t = 30 μs (c) t = 120 μs and (d) t = 1.0 ms.
A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.
How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
A capacitor of capacitance 12.0 μF is connected to a battery of emf 6.00 V and internal resistance 1.00 Ω through resistanceless leads. 12.0 μs after the connections are made, what will be (a) the current in the circuit (b) the power delivered by the battery (c) the power dissipated in heat and (d) the rate at which the energy stored in the capacitor is increasing?
Find the charge on each of the capacitors 0.20 ms after the switch S is closed in the figure.
Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.
A capacitor with stored energy 4⋅0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.
Obtain the expression for the energy stored in a capacitor connected across a dc battery.
A capacitor is charged by a battery and energy stored is 'U'. Now the battery is removed and the distance between plates is increased to four times. The energy stored becomes ______.
A 2µF capacitor is charge to 100 volt and then its plate are connected by a conducting wire. The heat produced is:-
What fraction of the energy drawn from the charging battery is stored in a capacitor?
A parallel plate capacitor has a uniform electric field `overset(->)("E")` in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is ______
(ε0 = permittivity of free space)
Do free electrons travel to region of higher potential or lower potential?
Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
Electrostatic energy of 4 x 10−4 J is stored in a charged 25 pF capacitor. Find the charge on the capacitor.
Derive an expression for energy stored in a capacitor.
In a capacitor of capacitance 20 µF, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
If the charge on the parallel plate capacitor is increased by 3 C, the energy stored in it increases by 44%. The original charge on the capacitor is ______.
A parallel combination of two capacitors of capacities ‘C’ and ‘`C/3`’ respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is Q1, Q2 and E1, E2 respectively. Then the ratio of (E1 − E2) to (Q1 − Q2) is ______.
