Questions 20 and 21 are based on the following write up A

Last updated: 6/13/2023

Questions 20 and 21 are based on the following write up A conducting balloon of radius a is charged to a potential Vo and held at a large height above the earth surface The large height of the balloon from the earth ensures that charge distribution on the surface of the balloon remains unaffected by the presence of the earth It is earthed through a resistance R and a valve is opened The gas inside the balloon escapes through the valve and the size of the balloon decreases The rate of decrease in radius of the balloon is controlled in such a manner that potential of the balloon remains constant Assume electric permittivity of the surrounding air equal to that of free space and charge does not leak to the surrounding air 20 Time rate at which radius r of the balloon changes is best represented by the expression a c 1 4 R r 4 R b a 0 5 av c 2 V d 1 4 R T 4 R 1 How much heat is dissipated in the resistance R until radius of the balloon becomes half b V d 4 V