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
Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
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?
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
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 capacitance C, a resistance R and an emf ε are connected in series at t = 0. What is the maximum value of (a) the potential difference across the resistor (b) the current in the circuit (c) the potential difference across the capacitor (d) the energy stored in the capacitor (e) the power delivered by the battery and (f) the power converted into heat?
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.
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 current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
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 C is connected to a battery of emf ε at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
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?
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
By evaluating ∫i2Rdt, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.
A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.
A large conducting plane has a surface charge density `1.0 xx 10^-4 "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.
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.
If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.
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.
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?
