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 (i) standard resistance and (ii) connecting wires in electric circuits?

Electron drift speed is estimated to be of the order of mm s–1. Yet large current of the order of few amperes can be set up in the wire. Explain briefly.

The current density j is related to electric field as j = σ E

Here, σ is the conductivity of the material. The above equation is equivalent to Ohm’s law.

Now, for a given material, σ is a constant. Hence, the plot of j versus E will be a straight line starting from the origin.

The slope of the graph is the conductivity of the material.

The graph with a greater slope is a better conductor and the graph with a lesser slope is a poor conductor as compare to the other.

• To make a standard resistance: A standard resistor should resist the current efficiently or allow the limited amount of current to pass through it. Hence, from the graph, the material whose plot is similar to plot (2) should be used to make a resistor.

• To make a connecting wire: A wire should allow all the current to flow through it without providing any resistance. So, it should have a higher conductivity. Hence, from the graph, the material whose plot is similar to plot (1) should be used to make a wire.

Electron drift is estimated to be of the order of mm s−1. However, the current set up in the wires is of the order of few amperes. This is because of the electron density which is very high in a material. It is of the order 10²⁸ per meter cube of the wire. Hence, all these electrons contribute to the total current. Therefore, even after the drift speed being small, the current set up in wires is large.