A copper wire and an -type silicon rod

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

Problem

A copper wire and an

n

-type silicon rod, each of length

1.0\,\text{m}

and cross-sectional area

1.0\,\text{mm}^2

, are connected in series to a battery so that the same steady current passes through both conductors. For copper, the number density of free electrons is

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

and the electron mobility is

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

. For the doped silicon, the number density of conduction electrons is

1.0 \times 10^{21}\,\text{m}^{-3}

and the electron mobility is

0.135\,\text{m}^2\text{V}^{-1}\text{s}^{-1}

. Take

e = 1.6 \times 10^{-19}\,\text{C}

. (i) If the current in the circuit is

1.0\,\text{mA}

, calculate the drift velocity of electrons in each conductor. (ii) Determine the magnitude of the electric field in each conductor. (iii) Hence obtain the ratio of the potential differences developed across the two conductors and state which one contributes more to the total emf of the battery.

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