(a) (i) Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence obtain an expression for it.

(ii) Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in $$\mathrm{A}$$ is 1.5 times that in $$\mathbf{B}$$. Find the ratio of drift velocity of electrons in wire A to that in wire. B.

OR

(b) (i) A cell emf of $$(\mathrm{E})$$ and internal resistance $$(\mathrm{r})$$ is connected across a variable load resistance (R). Draw plots showing the variation of terminal voltage $$V$$ with (i) $$R$$ and (ii) the current (I) in the load.

(ii) Three cells, each of emf $$\mathrm{E}$$ but internal resistances $$2 r, 3 r$$ and $$6 r$$ are connected in parallel across a resistor $$R$$.

Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential difference across the equivalent cell.

(a) Draw the circuit arrangement for studying V-I characteristics of a $$p$$-$$n$$ junction diode in (i) forward biasing and (ii) reverse biasing. Draw the typical V-I characteristics of a silicon diode. Describe briefly the following terms: (i) minority carrier injection in forward biasing and (ii) breakdown voltage in reverse biasing.

OR

(b) Name two important processes involved in the formation of a p-n junction diode. With the help of a circuit diagram, explain the working of junction diode as a full wave rectifier. Draw its input and output waveforms. State the characteristic property of a junction diode that makes it suitable for rectification.

(a) (i) Draw a ray diagram to show the working of a compound microscope. Obtain the expression for the total magnification for the final image to be formed at the near point.

(ii) In a compound microscope an object is placed at a distance of $$1.5 \mathrm{~cm}$$ from the objective of focal length $$1.25 \mathrm{~cm}$$. If the eye-piece has a focal length of $$5 \mathrm{~cm}$$ and the final image is formed at the near point, find the magnifying power of the microscope.

OR

(b) (i) Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.

(ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of $$150 \mathrm{~cm}$$. Find the focal lengths of the two lenses.

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between $$u, v$$ and $$f$$ for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

(i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image? If not, explain.

(ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed? Explain.

(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is $$20 \mathrm{~cm}$$.

OR

(iii) Two convex lenses A and B of focal lengths $$15 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively are placed coaxially '$$d$$' distance apart. A point object is kept at a distance of $$30 \mathrm{~cm}$$ in front of lens A. Find the value of '$$d$$' so that the rays emerging from lens $B$ are parallel to its principal axis.