Advertisements
Advertisements
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.
Advertisements
उत्तर
Initially charge on either capacitor is QA = QB = CV
After dielectric is introduced, new capacitance of either capacitor = KC
After opening switch potential across capacitor A is V volts.
Let potential across capacitor B be V1
Therefore QB = CV = C1V1 = KCV1
`"V"_1 = "V"/"K"`
Initial energy in both capacitors = `"CV"^2/2 + "CV"^2/2 = "CV"^2`
Final energy of capacitor A = `"KCV"^2/2`
Final energy of capacitor B = `"KCV"^2/"2K"^2 = "CV"^2/"2K"`
Total final energy of both capacitors = `"KCV"^2/2 + "CV"^2/"2K" = (("K"^2 + 1)/"2K") "CV"^2`
Ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric = `"CV"^2/((("K"^2 + 1)/"2K") "CV"^2) = "2K"/("K"^2 + 1)`
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
As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?
The outer cylinders of two cylindrical capacitors of capacitance 2⋅2 µF each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf 10 V is connected as shown in figure . Find the total charge supplied by the battery to the inner cylinders.
A 5⋅0 µF capacitor is charged to 12 V. The positive plate of this capacitor is now connected to the negative terminal of a 12 V battery and vice versa. Calculate the heat developed in the connecting wires.
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.
Derive the expression for resultant capacitance, when the capacitor is connected in parallel.
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system ______.
A 5µF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 µF capacitor If the energy change during the charge redistribution is `"X"/100`J then value of X to the 100 nearest integer is ______.
Calculate equivalent capacitance of the circuit shown in the Figure given below:
