Two straight metallic conductors P and Q

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

Two straight metallic conductors P and Q, of identical length and cross-section, are connected in parallel across the same direct-current source. (i) Show that the ratio of the currents carried by the two conductors is proportional to the product of the mobility and the free-electron density of each conductor. (ii) For conductor P (copper) the mobility is

4.5 \times 10^{-3}\,\text{m}^{2}\,\text{V}^{-1}\,\text{s}^{-1}

and the free-electron density is

8.5 \times 10^{28}\,\text{m}^{-3}

. For conductor Q (nickel) the corresponding values are

0.6 \times 10^{-3}\,\text{m}^{2}\,\text{V}^{-1}\,\text{s}^{-1}

and

9.1 \times 10^{28}\,\text{m}^{-3}

. Calculate the ratio

I_P : I_Q

of the currents when each conductor is

1.5\,\text{m}

long,

0.80\,\text{mm}^{2}

in area, and the applied potential difference is

3.0\,\text{V}

. (iii) Determine the ratio of the drift velocities of electrons in the two conductors under the conditions of part (ii).

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