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Both the capacitors shown in figure are made of square plates of edge a. The separations between the plates of the capacitors are d1 and d2 as shown in the figure. A potential difference V is applied between the points a and b. An electron is projected between the plates of the upper capacitor along the central line. With what minimum speed should the electron be projected so that it does not collide with any plate? Consider only the electric forces.
The plates of a capacitor are 2.00 cm apart. An electron-proton pair is released somewhere in the gap between the plates and it is found that the proton reaches the negative plate at the same time as the electron reaches the positive plate. At what distance from the negative plate was the pair released?
A finite ladder is constructed by connecting several sections of 2 μF, 4 μF capacitor combinations as shown in 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 of capacitance 2.0 μF is charged to a potential difference of 12V. 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 use capacitor to the other.
A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1.00 mm is connected to a battery of 12.0 V. The plates are pulled apart to increase the separation to 2.0 mm.
a) Calculate the charge flown through the circuit during the process.
b) How much energy is absorbed by the battery during the process?
c) Calculate the stored energy in the electric field before and after the process.
d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart.
e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.
A capacitor having a capacitance of 100 μF is charged to a potential difference of 24V. The charging battery is disconnected and the capacitor is connected to another battery of emf 12V with the positive plate of the capacitor joined with the positive terminal of the battery.
a) Find the charges on the capacitor before and after the reconnection.
b) Find the charge flown through the 12V battery.
c) Is work done by the battery or is it done on the battery? Find its magnitude.
d) Find the decrease in electrostatic field energy.
e) Find the heat developed during the flow of charge after reconnection.
Consider the situation shown in figure. The switch S is open for a long time and then closed.
a) Find the charge flown through the battery when the switch S is closed.
b) Find the work done by the battery.
c) Find the change in energy stored in the capacitors.
d) Find the heat developed in the system.
A capacitor of capacitance 5.00 μF is charged to 24.0V and another capacitor of capacitance 6.0 μF is charged to 12.0V.
a) Find the energy stored in each capacitor.
b) The positive plate of the first capacitor is now connected to the negative plate of the second nd vice versa. Find the new charges on the capacitors.
c) Find the loss of electrostatic energy during the process.
d) Where does this energy go?
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.
A parallel-plate capacitor of capacitance 5 μF is connected to a battery of emf 6V. The separation between the plates is 2 mm.
a) Find the charge on the positive plate.
b) Find the electric field between the plates.
c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination.
d) How much charge has flown through the battery after the slab is inserted?
A parallel-plate capacitor having plate area 400 cm2 and separation between the plates 1.0 mm is connected to a power supply of 100V. A dielectric slab of thickness 1.0 mm and dielectric constant 5.0 is inserted into the gap.
a) Find the increase in electrostatic energy.
b) If the power supply is now disconnected and the dielectric slab is taken out, find the further increase in energy.
c) Why does the energy increase in inserting the slab as well as in taking it out?
Shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.
A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.
A capacitor having a capacitance of 100 μF is charged to a potential difference 50V.
a) What is the magnitude of the charge on each plate?
b) The charging battery is disconnected and a dielectric of dielectric constant 2.5 is inserted. Calculate the new potential difference between the plates.
c) What charge would have produced this potential difference in absence of the dielectric slab.
d) Find the charge induced at a surface of the dielectric slab.
Figure shows two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is the same for the two capacitors. The plates are rectangular in shape with width b and lengths ℓ1 and ℓ2. The left half of the dielectric slab has a dielectric constant K1 and the right half K2. Neglecting any friction, find the ratio of the emf of the left battery to that of the right battery for which the dielectric slab may remain in equilibrium.
Consider the situation shown in figure.
The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.