A capacitor of capacity C is charged by connecting it with R according to the figure. Energy supplied by the battery in this process is :

• more than $\frac{1}{2}C{V}^2$

• $\frac{1}{2}{\mathrm{CV}}^2$

• 2CV²

• less than $\frac{1}{2}{\mathrm{CV}}^2$

Two capacitors, one 4 pF and the other 6 pF, connected in parallel, are charged by a 100 V battery. The energy stored in the capacitors is

• 1.2 × 10⁻⁸ J

• 2.4 × 10⁻⁸ J

• 5.0 × 10⁻⁸ J

• 1.2 × 10⁻⁶ J 

If the energy of a 100 $\mathrm{\mu }$F capacitor charged to 6 kV could all be used to lift a 5O kg mass, what would be the greatest vertical height through which mass could be raised?

• 0.6 mm

• 3.6 m

• 1.2 mm

• 12 m

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

• decreases

• remains unchanged

• becomes infinite

• increases

The diameter of each plate of an air capacitor is 4 cm. To make the capacity of this plate capacitor equal to that of 20 cm diameter sphere, the distance between the plates will be

• 4 × 10^-3 m

• 1 × 10^-3 m

• 1 cm

• 1 × 10^-3 cm

The electric potential V is given as a function of distance x (m) by V = (5x² + 10x − 9) volt. Value of electric field at x=l m is

• 20 V/m

• 6 V/m

• 11 V/m

• − 23 V/m

Three charged particles are initially in position-1. They are free to move and they come to position-2, after some time. Let U₁ and U₂ be the electrostatic potential energies in position-1 and 2 then

• U₁ = U₂

• U₂ $\ge$ U₁

• U₂ > U₁

• U₁ > U₂

Three capacitors of 3, 2 and 6 µF are connected in series with a battery of 10 V. Then charge on 3 µF capacitor will be

• 10 µC

• 12 µC

• 14 µC

• 5 µC

Equivalent capacity between A and B is

• 2 µF

• 3 µF

• 4 µF

• 0.5 µF

What is the area of the plate of a 3 F parallel plate capacitor, if the separation between the plates is 5 mm?

• 12.981 x 10² m²

• 9.281 × 10⁹ m²

• 1.69 × 10¹² m²

• 4.529 × 10⁹ m²