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 .

Capacitors P and Q have identical cross sectional areas A and separation d. The space between the capacitors is filled with a dielectric of dielectric constant epsilon_(r) as shown in the figure . Calculate the capacitance of capacitors P and Q .

A parallel plate capacitor has plate area A and plate separation d. The space between the plates is filled up to a thickness x (ltd) with a dielectric constant K. Calculate the capacitance of the system.

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

Figure shown a parallel-plate capacitor having square plates of edge a and plate-separation d. The gap between the plates is filled with a dielectric of dielectric constant K which varies parallel to an edge as where K and a are constants and x is the distance from the left end. Calculate the capacitance.

Assertion , A parallel plate capacitor is charged by a battery, when battery is disconnected , if the space between the plates is filled with a dieelectric, then energy stored will increase. Reason : Due to the introduction of dielectric the capacitance will be increased.

Figure shows two identical parallel plate capacitors connected to 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.

Two parallel plate capacitors, each of capacitance 40 muF , are connected is series. The space between the plates of one capacitor is filled with a dielectric material of dielectric constant K =4. Find the equivalent capacitacne of the system.

Suppose the space between the two inner shells of the previous problem is filled with a dielectric constant . K. Find the capacitance of the system between A and B.