Electrostatic Potential and Capacitance

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity 1 1013 Ωm and resistance 17.7 1014 Ω. Relative permittivity of the insulating material is 107. The value of is . (Take permittivity of free space =8.85 10-12 F/m)

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant K=5, the percentage increase in the capacitance is . [figure]

1. 33.34
2. 66.67
3. 200
4. 400

Three parallel plate capacitors each with area A and separation d are filled with two dielectrics (k1 and k2) in the following fashion. Which of the following is true? (k1 > k2) [figure]

1. CC > CB > CA
2. CB > CC > CA
3. CA > CC > CB
4. CC > CA > CB

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K1 = 2, K2 = 3 and K3 = 5 (as shown in figure). If new capacitance is n3C then the value of n is . [figure]

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25\% more charge from the battery. The dielectric constant of mica is

1. 1.0
2. 2.5
3. 1.5
4. 2.0

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ( 13 )rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

1. 3CK2(2K+1)2
2. 4KC3K-1
3. CK2+K
4. 3KC2K+1

[figure] Space between the plates of a parallel plate capacitor of plate area 4 cm2 and separation of 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is pF. (Given 0 = 8.85 10-12 F/m)

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants 1 and 2, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are C1 and C2 respectively, then C1C2 is: First Configuration [figure] Second Configuration [figure]

1. 0( 1 + 2)2
2. 1 22( 1 + 2)2
3. 4 1 2( 1 + 2)2
4. 1 2 1 + 2

A parallel-plate capacitor of capacitance 40 is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K=2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

1. 8 mC and 2.0 J
2. 4 mC and 0.2 J
3. 2 mC and 0.2 J
4. 2 mC and 0.4 J

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]

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 .