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
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions
Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 μF. When the ends X and Y are connected to a 6 V battery, find out (i) the charge and (ii) the energy stored in the network.
Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are
Find the capacitance of the combination shown in figure between A and B.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
A capacitor of capacitance 2⋅0 µF is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance 4⋅0 µF as shown in figure . Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Two spherical conductors A and B of radii a and b(b > a) are placed concentrically in the air. B is given a charge +Q and A is earthed. The equivalent capacitance of the system is ______.
A capacitor with capacitance 5µF is charged to 5 µC. If the plates are pulled apart to reduce the capacitance to 2 µF, how much work is done?
