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.

A series CR circuit with $$R=200 \Omega$$ and $$C=(50 / \pi)$$ $$\mu \mathrm{F}$$ is connected across an ac source of peak voltage $$\varepsilon_0=100 \mathrm{~V}$$ and frequency $$v=50 \mathrm{~Hz}$$. Calculate (a) impedance of the circuit $$(\mathrm{Z})$$, (b) phase angle $$(\phi)$$, and (c) voltage across the resistor.

Define critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.

(a) (i) Distinguish between nuclear fission and fusion giving an example of each.

(ii) Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.

OR

(b) (i) How is the size of a nucleus found experimentally? Write the relation between the radius and mass number of a nucleus.

(ii) Prove that the density of a nucleus is independent of its mass number.