Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Show that average value of radiant flux density ‘S’ over a single period ‘T’ is given by S = `1/(2cmu_0) E_0^2`.

You are given a 2 µF parallel plate capacitor. How would you establish an instantaneous displacement current of 1 mA in the space between its plates?

Sea water at frequency ν = 4 × 10⁸ Hz has permittivity ε ≈ 80 εo, permeability µ ≈ µo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in seawater and driven by an alternating voltage source V(t) = V_o sin (2πνt). What fraction of the conduction current density is the displacement current density?

A long straight cable of length `l` is placed symmetrically along z-axis and has radius a(<< l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t) = I₀ sin (2πνt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s,t) = µ₀I₀ν cos (2πνt) In `(s/a)hatk`.

1. Calculate the displacement current density inside the cable.
2. Integrate the displacement current density across the cross-section of the cable to find the total displacement current I^d.
3. Compare the conduction current I0 with the displacement current `I_0^d`.

You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of yellow light is replaced with that of other lights without changing the angle of incidence?

The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will ______.

The direction of ray of light incident on a concave mirror is shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked 1, 2, 3 and 4 (figure). Which of the four rays correctly shows the direction of reflected ray?

A car is moving with at a constant speed of 60 km h^–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h^–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?

An astronomical refractive telescope has an objective of focal length 20 m and an eyepiece of focal length 2 cm.

1. The length of the telescope tube is 20.02 m.
2. The magnification is 1000.
3. The image formed is inverted.
4. An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L << |v – f|.

A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0, 0) and an object placed at (– 50 cm, 0). Find the coordinates of the image.

(i) Consider a thin lens placed between a source (S) and an observer (O) (Figure). Let the thickness of the lens vary as `w(b) = w_0 - b^2/α`, where b is the verticle distance from the pole. `w_0` is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.

(ii) A gravitational lens may be assumed to have a varying width of the form

`w(b) = k_1ln(k_2/b) b_("min") < b < b_("max")`

= `k_1ln (K_2/b_("min")) b < b_("min")`

Show that an observer will see an image of a point object as a ring about the center of the lens with an angular radius

`β = sqrt((n - 1)k_1 u/v)/(u + v)`

Figure shows a standard two slit arrangement with slits S₁, S₂, P₁, P₂ are the two minima points on either side of P (Figure). At P₂ on the screen, there is a hole and behind P₂ is a second 2-slit arrangement with slits S₃, S₄ and a second screen behind them.

For light diverging from a point source ______.

1. the wavefront is spherical.
2. the intensity decreases in proportion to the distance squared.
3. the wavefront is parabolic.
4. the intensity at the wavefront does not depend on the distance.

Is Huygen’s principle valid for longitudinal sound waves?

Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is the nature of the wavefronts emerging from the final image?

What is the shape of the wavefront on earth for sunlight?

Consider Figure for photoemission.

How would you reconcile with momentum conservation? Note light (photons) have momentum in a different direction than the emitted electrons.

O₂ molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms ______.

Would the Bohr formula for the H-atom remain unchanged if proton had a charge (+4/3)e and electron a charge (−3/4)e, where e = 1.6 × 10^–19C. Give reasons for your answer.