Advertisements
Advertisements
प्रश्न
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 total electrostatic energy stored in A and B finally and that stored in A initially.
Advertisements
उत्तर
The electric field in the region between the plates depends on the change given to the conducting plates,
For capacitor 'A' of capacitance C, having voltage V, the charge on it is given by Q = CV.
On connecting this capacitor A with capacitor B changes get distributed.
The total electrostatic energy stored in A is given by
`U_A = 1/2CV^2 = 1/2 Q^2/C` .........(i)
Since capacitor B is connected across capacitor A.
∴ `C_"net" = C_A + C_B`
= C + 2C
= 3C
∴ Total electrostatic energy in A and B is given by
`U_"net" = 1/2 Q^2/C_"net"`
= `1/2(Q^2/(3C))` ....(since total change Q remains constant)
= `1/3(1/2 Q^2/C)`
= `1/3U_A` .....[By equation (i)]
`U_"net"/U_A = 1/3`
APPEARS IN
संबंधित प्रश्न
Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
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.
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.
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.
A capacitor is a device that stores ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
An air-filled 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 ______
(∈0 = permittivity of free space)
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 ______.
