Electrostatic Potential and Capacitance

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 .

The distance between charges +q and -q is 2l and between +2q and -2q is 4l. The electrostatic potential at point P at a distance r from center O is - [ qlr2 ] 109 V, where the value of is . (Use 14 0=9 109 Nm2C-2) [figure]

The electrostatic potential due to an electric dipole at a distance 'r' varies as :

1. 1r3
2. 1r
3. 1r2
4. r

A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2C and potential 2V. Then the loss of energy is x3E, where x is .

A 16 wire is bent to form a square loop. A 9 V battery with internal resistance 1 is connected across one of its sides. If a 4 capacitor is connected across one of its diagonals, the energy stored by the capacitor will be x2 , where x=

An electric charge 10-6 is placed at origin (0,0) m of X − Y co-ordinate system. Two points P and Q are situated at ( 3, 3) m and ( 6,0) m respectively. The potential difference between the points P and Q will be :

1. 3 V
2. 6 V
3. 0 V
4. 3 V