Figure shows a potentiometer with a cell of 2.0 V and internal resistance $0.40\Omega$ maintaining  a  potential  drop  across  the  resistor  wire AB. A  standard  cell  which  maintains  a constant  emf  of  1.02  V (for  very moderate  currents  up to a  few mA) gives  a balance  point  at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 k$\Omega$ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf and the balance point found similarly, turns out to be at 82.3 cm length of the wire.(a) What is the value $\epsilon$?(b) What purpose does the high resistance of 600 k $\Omega$ have?(c) Is the balance point affected by this high resistance? (d) Is the balance point affected by the internal resistance of the driver cell?(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0 V instead of 2.0 V?(f) Would the circuit work well for detering an extremely small emf, say of the order of a few mV (such as the typical emf of a thermo-couple)? If not, how will you modify the circuit?

(a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0\times 10^{-7}{\mathrm{m}}^2$ carrying a current of $1.5\mathrm{A}$. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0\times 10^3\mathrm{kg}/{\mathrm{m}}^3$, and its atomic mass is $63.5\mathrm{u}$. (b) Compare the drift speed obtained above with, (i) thermal speeds of copper atoms at ordinary temperatures, (ii) speed of propagation of electric field along the conductor which causes the drift motion.