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 (i) standard resistance and (ii) connecting wires in electric circuits?
Electron drift speed is estimated to be of the order of \[{\rm{mm}}{{\rm{s}}^{ - 1}}\]. Yet large current of the order of few amperes can be set up in the wire, Explain briefly.

Answer 1

Hint: From the concept of current density we can say that current density is given by the charge flow with respect to time and area of cross-section of a material. In order words we can say that higher the value of current density, greater will be the conductivity of the material.

Complete step by step answer:
We know that current density of a material can be expressed as the product of its conductivity and the value of electric field to which material is subjected so we can write:
\[J = \sigma E\]
Here J is the current density, \[\sigma \] is the conductivity of material and E is the electric field.

We know that the value of conductivity for a material is fixed so it can be assumed as a constant value, therefore we can write the above expression as a linear relationship between current density and electric field.
\[J \propto E\]……(1)

Based on the above expression, we can conclude that current density will vary linearly with electric field and it will have a linear slope on current density-electric field plot. We can represent the slope of two different materials on the graph as below:

In order to make a standard resistance we know that it should resist the flow of current that means its slope should be the same as material 2.

We know that the conductivity of a connecting wire should be high so that it can allow current easily to pass through it without minimum losses so the slope of material similar to slope of material 1 can be considered to make connecting wire.

It is given that the drift velocity of electrons is of the order of millimetres per second even though the current is having a value of few amperes so this means that the value of current density is very high for that material. All electrons present take place in flow of current; therefore, with small drift velocity the current in wires has a higher value.

Note:
We can assume equation (1) similar to the expression of Ohm’s law that the voltage across a material is linearly proportional to its resistance. We can note that current also depends on the number of electrons taking place in the flow of current.