Advertisements
Advertisements
प्रश्न
Obtain the expression for energy stored in the parallel plate capacitor.
Advertisements
उत्तर
- Capacitor not only stores the charge but also stores energy.
- When a battery is connected to the capacitor, electrons of total charge -Q are transferred from one plate to the other plate.
- To transfer the charge, work is done by the battery. This work done is stored as electrostatic potential energy in the capacitor.
- To transfer an infinitesimal charge dQ for a potential difference V, the work done is given by
dW = V dQ ………….(1)
where V = `"Q"/"C"`
The total work done to charge a capacitor is
W = `int_0^"Q" "Q"/"C" "dQ" = "Q"^2/"2C"` .....(2)
This work done is stored as electrostatic potential energy (UB) in the capacitor.
`"U"_"E" = "Q"^2/"2C" = 1/2 "CV"^2` ....(3)
where Q = CV is used. - This stored energy is thus directly proportional to the capacitance of the capacitor and the square of the voltage between the plates of the capacitor.
`"U"_"E" = 1/2 ((ε_0"A")/"d")("Ed")^2 = 1/2 ε_0 ("Ad")"E"^2` ....(4)
where Ad = volume of the space between the capacitor plates. The energy stored per unit volume of space is defined `"U"_"E" = 1/2ε_0 "E"^2` .....(5) - Energy is stored in the electric field existing between the plates of the capacitor. 0nce the capacitor is allowed to discharge, the energy is retrieved.
- The energy density depends only on the electric field and not on the size of the plates of the capacitor.
APPEARS IN
संबंधित प्रश्न
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.
Find the equivalent capacitances of the combinations shown in figure between the indicated points.
A finite ladder is constructed by connecting several sections of 2 µF, 4 µF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?
A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure . Find the capacitance.
Three capacitors C1 = 3μF, C2 = 6μF, and C3 = 10μF are connected to a 50 V battery as shown in Figure below:
Calculate:
(i) The equivalent capacitance of the circuit between points A and B.
(ii) The charge on C1.
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.
Derive the expression for resultant capacitance, when the capacitor is connected in series.
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 ______.
