Electrostatic Potential and Capacitance

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is A3 and the height is d, the capacitance of the arrangement is : [figure]

1. 11 0 A20 d
2. 13 0 A17 d
3. 18 0 A11 d
4. 11 0 A18 d

At the centre of a half ring of radius R = 10 cm and linear charge density 4 nC m-1, the potential is x V. The value of x is .

Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

1. ab
2. ba
3. ab
4. ab

A capacitor has air as dielectric medium and two conducting plates of area 12 cm2 and they are 0.6 cm apart. When a slab of dielectric having area 12 cm2 and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given 0 = 8.834 10-12 F/m)

1. 1.50
2. 0.66
3. 1.33
4. 1

A capacitor of 10 capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8 N. The supply voltage is V. [figure]

Three capacitors of capacitances 25 , 30 and 45 are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is 9xE. The value of x is .

A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected between its plates to potential difference of 12.0 V. The battery is now disconnected and a dielectric slab ( r = 6) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is 10-12 J.

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

1. 14CV2
2. 34CV2
3. 12CV2
4. 2CV2

A galvanometer (G) of 2 resistance is connected in the given circuit. The ratio of charge stored in C1 and C2 is : [figure]

1. 1
2. 23
3. 32
4. 12

A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25\% more charge from the battery than before. The dielectric constant of the sheet is .