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
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
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 charged to a potential V. The flux of the electric field through a closed surface enclosing the capacitor is
Suppose, one wishes to construct a 1⋅0 farad capacitor using circular discs. If the separation between the discs be kept at 1⋅0 mm, what would be the radius of the discs?
Find the charges on the three capacitors connected to a battery as shown in figure.
Take `C_1 = 2.0 uF , C_2 = 4.0 uF , C_3 = 6.0 uF and V` = 12 volts.
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
Find the equivalent capacitances of the combinations shown in figure between the indicated points.
The separation between the plates of a parallel-plate capacitor is 0⋅500 cm and its plate area is 100 cm2. A 0⋅400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.
Suppose the space between the two inner shells is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.
Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.
