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 three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E=2x i+3y2 j+4 k N/C. The work done in moving the charge is J.

The electric potential as a function of x, y is given by V=5 (x2-y2 ) V. The electric field at a point (2, 3) m is V/m.

1. (-20 i+30 j )
2. (20 i-30 j )
3. (20 i+45 j )
4. (-4 i+6 j )

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is 10-7 J. The value of is . (combined capacitance of spheres is 200 pF)

1. 5
2. 52
3. 72
4. 92

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to x , where is .

1. -2
2. 1
3. -1
4. 2

From the circuit given below, the capacitance between terminals A and B shown in the circuit is μF. (take C1=C2=C3=1 μF and C4=2 μF.) [figure]

1. 2
2. 7/2
3. 7/3
4. 5/2

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Choose the correct answer from the options given below :

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

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

Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1 and S2 spheres are ES1 and ES2 respectively. The value of ES1ES2 is .

1. 32
2. 23
3. 49
4. 94

Two metal plates (A, B) are kept horizontally with separation of ( 12 ) cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm3) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials VA and VB are required on plates A and B respectively in order to ensure the droplets do not descend. The values of VA and VB are . (Neglect the air resistance to the droplets and take g=10 m/s2)

1. 100 V and 580 V
2. 580 V and 100 V
3. 60 V and 400 V
4. 0 V and -200 V