Question

Plot a graph showing the variation of current density ( $j$ ) versus the electric field ( $E$ ) for two conductors of different materials. What information from this plot regarding the properties of the conducting material, can be obtained which can be used to select suitable materials for use in making connecting wires in electric circuits?

Electron drift speed is estimated to be of the order of $mm s^{- 1}$ . Yet a large current of the order of few amperes can be set up in the wire. Explain briefly.

Accepted Answer

As $j = σ E$ , so the graph of current density ( $j$ ) versus electric field ( $E$ ) for any material is a straight line, as shown in the figure.

Slope of the graph $=$ Conductivity $(σ)$

The material $B$ with less slope (smaller conductivity or higher resistivity) is used for making standard resistances while the material $A$ with greater slope (higher conductivity) for making connecting wires.

Electric current, $I = e n A v_{d}$

Although both $e$ and $v_{d}$ are very small, yet we can obtain a large current. This is because free electron density of a conductor is very large, $n ≃ 10^{23} m^{- 3}$ . The drifts of a very large number of free electrons add up to cause a large current inside the conductor.

S L Arora Solutions for Chapter: Current Electricity, Exercise 3: SHORT ANSWER CONCEPTUAL PROBLEMS

S L Arora Physics Solutions for Exercise - S L Arora Solutions for Chapter: Current Electricity, Exercise 3: SHORT ANSWER CONCEPTUAL PROBLEMS

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