Topic ; Resistance

It may be defined as the property of a substance due to which it opposes (or restricts) the flow of electricity (i.e., electrons) through it.

Metals (as a class), acids and salts solutions are good conductors of electricity.  Amongst pure metals, silver, copper and aluminium are very good conductors in the given order.*  This, as discussed earlier, is due to the presence of a large number of free or loosely-attached electrons in their atoms.  These vagrant electrons assume a directed motion on the application of an electric potential difference.  These electrons while flowing pass through the molecules or the atoms of the conductor, collide and other atoms and electrons, thereby producing heat.

Those substances which offer relatively greater difficulty or hindrance to the passage of these electrons are said to be relatively poor conductors of electricity like bakelite, mica, glass, rubber, p.v.c. (polyvinyl chloride) and dry wood etc.  Amongst good insulators can be included fibrous  substances such as paper and cotton when dry, mineral oils free from acids and water, ceramics like hard porcelain and asbestos and many other plastics besides p.v.c.  It is helpful to remember that electric friction is similar to friction in Mechanics

 The Unit of Resistance ;

The practical unit of resistance is ohm.**  A conductor is said to have a resistance of one ohm if it permits one ampere current to flow through it when one volt is impressed across its terminals. For insulators whose resistances are very high, a much bigger unit is used i.e., mega-ohm = 106 ohm (the prefix ‘mega’ or mego meaning a million) or kilo-ohm = 103 ohm (kilo means thousand).  In the case of very small resistances, smaller units like milli-ohm = 10− 3 ohm or micro-ohm = 10− 6 ohm are used.  The symbol for ohm is Ω.

* However, for the same resistance per unit length, cross-sectional area of aluminium conductor has to be 1.6 times that of the copper conductor but it weighs only half as much.  Hence, it is used where economy of weight is more important than economy of space.

 ** After George Simon Ohm (1787-1854), a German mathematician who in about 1827 formulated the law known after his name as Ohm’s Law.

Table 1.1.  Multiples and Sub-multiples of Ohm

Prefix                Its meaning                 Abbreviation             Equal to 

 Mega-               One million                      M Ω                    106 Ω

 Kilo-               One thousand                      k Ω                      103 Ω 

 Centi-            One hundredth –

 Milli-              One thousandth                   m Ω                     10−3 Ω

 Micro-             One millionth                      μ Ω                     10−6 Ω

  Laws of Resistance 

The resistance R offered by a conductor depends on the following factors :

 (i) It varies directly as its length, l.

 (ii) It varies inversely as the cross-section A of the conductor.

(iii) It depends on the nature of the material.

(iv) It also depends on the temperature of the conductor

Neglecting the last factor for the time being, we can say that...

R ∝ l/ A or R =  ρ 1/A..............(i)

where ρ is a constant depending on the nature of the material of the conductor and is known as its specific resistance or resistivity. 

If in Eq. (i), we put

                              l = 1 metre and A = 1 metre2, then R = ρ (Fig. 1.4) 

Hence, specific resistance of a material may be defined as the resistance between the opposite faces of a metre cube of that material.