State the basic principle behind the working of an ac generator. Briefly describe its working and obtain the expression for the instantaneous value of emf induced.

(a) Briefly describe how the current sensitivity of a moving coil galvanometer can be increased.

(b) A galvanometer shows full scale deflection for current $$I_g$$. A resistance $$R_1$$ is required to convert it into a voltmeter of range $$(0-V)$$ and a resistance $$R_2$$ to convert it into a voltmeter of range $$(0-2 \mathrm{~V})$$. Find the resistance of the galvanometer.

(a) (i) Differentiate between 'distance of closest approach' and 'impact parameter'.

(ii) Determine the distance of closest approach when an alpha particle of kinetic energy 3.95 $$\mathrm{MeV}$$ approaches a nucleus of $$Z=79$$, stops and reverses its directions.

OR

(b) (i) State three postulates of Bohr's theory of hydrogen atom.

(ii) Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.

(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.