# Current Electricity - III

Electrical Conductivity:

where s is a constant of proportionality called electrical conductivity. This statement is one possible form of Ohm’s law.

Consider a cylindrical material with cross sectional area A and length L through which a current is passing along the length and normal to

Where A is cross sectional area and L is length of

the material through which a current is passing along the length, normal to the area A. But, JA = I, the current through the area A and EL = V1 - V2, the potential difference across the ends of the cylinder denoting V1-V2 as V,

as a linear relationship between the potential drop across a substance and the current passing through it.

Measuring resistance:
EMF:

Emf (Electromotive force) is the name given to a non-electrostatic agency. Typically, it is a battery, in which a chemical process achieves this task of doing work in driving the positive charge from a low potential to a high potential. The effect of such a source is measured in terms of work done per unit charge in moving a charge once around the circuit. This is denoted by Î.

Significance of Ohm’s Law:

Ohm’s law is obeyed by many substances, but it is not a fundamental law of nature. It fails if

a)V depends on I non- linearly. Example is when ρ increases with I (even if temperature is kept fixed).

b)The relation between V and I depends on the sign of V for the same absolute value of V.

c)The relation between V and I is non- unique. For e.g., GaAs

An example of (a) & (b) is of a rectifier

When a source of emf[(e )] is connected to an external resistance R, the voltage Vext across R is given by

Where r is the internal resistance of the source.

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