(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.