Science (English Medium) Class 12 - CBSE Question Bank Solutions

A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge`Q/2` is placed at its centre C and an other charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.

A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?

The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.

With the help of necessary circuit diagram, describe briefly how n-p-n transistor in CE configuration amplifies a small sinusoidal input voltage. Write the expression for the ac current gain

Under what condition does the transistor act as an amplifier?

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10⁻²² C/m2. What is E:

1. in the outer region of the first plate,
2. in the outer region of the second plate, and
3. between the plates?

Three capacitors each of capacitance 9 pF are connected in series.

1. What is the total capacitance of the combination?
2. What is the potential difference across each capacitor if the combination is connected to a 120 V supply?

Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. Determine the charge on each capacitor if the combination is connected to a 100 V supply.

An electrical technician requires a capacitance of 2 µF in a circuit across a potential difference of 1 kV. A large number of 1 µF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.

A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

Derive an expression for voltage gain of the amplifier and hence show that the output voltage is in opposite phase with the input voltage.

How is linearly polarised light obtained by the process of scattering of light. Find the Brewster angle for air – glass interface, when the refractive index of glass = 1.5. 

Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C₁ and C₂ with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.

An infinitely large thin plane sheet has a uniform surface charge density +σ. Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet. 

Distinguish between unpolarized light and linearly polarized light

Draw a circuit diagram for studying the input and output characteristics of a n-p-n transistor in common emitter configuration. Using the circuit, explain how input, output characteristics are obtained

Draw a graph showing the variation of intensity (I) of polarised light transmitted by an analyzer with the angle (θ) between polariser and analyzer.

A bar magnet of magnetic moment 6 J/T is aligned at 60° with a uniform external magnetic field of 0·44 T Calculate  

a) the work done in turning the magnet to align its magnetic moment

i) normal to the magnetic field, 

ii) opposite to the magnetic field, and

b)  the torque on the magnet in the final orientation in case (ii).

Using Gauss's law in electrostatics, deduce an expression for electric field intensity due to a uniformly charged infinite plane sheet. If another identical sheet is placed parallel to it, show that there is no electric field in the region between the two sheets ?

A point object is placed on the principal axis of a convex spherical surface of radius of curvature R, which separates the two media of refractive indices n₁ and n₂ (n₂ > n₁). Draw the ray diagram and deduce the relation between the object distance (u), image distance (v) and the radius of curvature (R) for refraction to take place at the convex spherical surface from rarer to denser medium.