A sphercial capacitor is made of two conducting spherical shells of radii a and b.The space between the shells is filled with a dielectric constant `K`up to a radius c as shown in figure. Calculate the capacitance .

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32. (a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere? (c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d_(1) and dielectric constant k_(1) and the other has thickness d_(2) and dielectric constant k_(2) as shown in figure. This arrangement can be thought as a dielectric slab of thickness d = ( d_(1) + d_(2) ) and effective dielectric constant k. The k is ...... (a) (K_(1)d_(1)+K_(2)d_(2))/(d_(1)+d_(2)) (b) (K_(1)d_(1)+K_(2)d_(2))/(K_(1)+K_(2)) (c) (K_(1)K_(2)(d_(1)+d_(2)))/((K_(1)d_(2)+K_(2)d_(1))) (d) (2K_(1)K_(2))/(K_(1)+K_(2))

Three concentric conducting spherical shells have radii r, 2r, and 3r and charges q_1,q_2 and q_3 , respectively. Innermost and outermost shells are earthed as shown in figure. The charges shown are after earthing. Select the correct alternative.

A parallel plate air capacitor of capacitance C is connected to a cell o f emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

A wire of resistance 12 Omega m^(-1) is bent to from a complete circle of radius 10 cm . The resistance between its two diametrically opposite points, A and B as shown in the figure, is

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Consider the partition to be rigidly fixed so that it does not move. when equilibrium is achieved, the final temperature of the gases will be

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. the total work done by the gases till the time they achieve equilibrium will be

Figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. Calculate the capacitance and the rate of change of potential difference between the plates.

Two conducting hollow spherical shells of radius R and 2R carry charges -Q and 3Q respectively. How much charge will flow into the earth if inner shell is grounded?