Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given :
Energy stored in the charged capacitor = 4.0 J
When the capacitors are connected, the charge flows from the charged capacitor to the uncharged capacitor. Because the capacitors are identical, the charge flows till the charge in both the capacitors becomes equal.
The energy of a capacitor is given by `E = q^2/(2C)`
As the charge in both the capacitors is the same, their capacitance is also the same. So, the energy is equally divided between them.
Thus, the energy stored in each of the capacitors is 2.0 J.
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?
In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :
(i) Energy stored in 12 µF capacitor.
(ii) Energy stored in 3 µF capacitor.
(iii) Total energy drawn from the battery.

Find the charge on the capacitor as shown in the circuit.

The energy density in the electric field created by a point charge falls off with the distance from the point charge as
A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
(a) The current in each of the two discharging circuits is zero at t = 0.
(b) The currents in the two discharging circuits at t = 0 are equal but not zero.
(c) The currents in the two discharging circuits at t = 0 are unequal.
(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.
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?
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?
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 capacitor of capacitance 100 μF is connected across a battery of emf 6 V through a resistance of 20 kΩ for 4 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4 s after the battery is disconnected?
Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.
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 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 ______.
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)
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.
