Electrostatic Potential and Capacitance

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

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is . 14 0 = 9 109 N m2/C2

1. 3.3
2. 27
3. 2.7
4. 5.4

Which one of the following is not a measurable quantity?

1. Resistance
2. Voltage difference
3. Displacement current
4. Voltage

Identify the correct statements : Choose the correct answer from the options given below :

1. A, C and D Only
2. A, B and C Only
3. B and D Only
4. C and D Only

There are three concentric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charges q1, q2 and q3 respectively. The potentials of the spheres A, B and C respectively, are :

1. 14 0 ( q1a + q2b + q3c ), 14 0 ( q1 + q2 + q3b ), 14 0 ( q1 + q2 + q3c )
2. 14 0 ( q1 + q2 + q3a ), 14 0 ( q1 + q2 + q3b ), 14 0 ( q1 + q2 + q3c )
3. 14 0 ( q1 + q2 + q3a ), 14 0 ( q1 + q2b + q3c ), 14 0 ( q1a + q2b + q3c )
4. 14 0 ( q1a + q2b + q3c ), 14 0 ( q1 + q2b + q3c ), 14 0 ( q1 + q2 + q3c )

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]