Draw energy band diagram for an $$n$$-type and $$p$$-type semiconductor at $$\mathrm{T}>0 \mathrm{~K}$$.

Answer the following giving reasons:

(i) A $$p$$-$$n$$ junction diode is damaged by a strong current.

(ii) Impurities are added in intrinsic semiconductors.

(a) Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a wire. Find the ratio of the electric fields at their surfaces.

OR

(b) A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage $$V$$. The battery is disconnected and an uncharged capacitor (B) of capacitance $$2 \mathrm{C}$$ is connected across $$\mathrm{A}$$. Find the ratio of

(i) final charges on A and B.

(ii) total electrostatic energy stored in A and B finally and that stored in A initially.

Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the conductor and relaxation time.