The property of a substance which opposes the flow of current through it is called its resistance. In Eq. 16.2, it can be seen that for a certain value of potential V, if the value of R is increased, then the current I would be small. It means the opposition to flow of current is large. On the other hand. If R is small, the current would be large which means that the opposition to flow of current is small. Thus the proportionality constant R in Eq. 16.2 is a measure of the resistance of the conductor. Its value can be determined by the V-I graph.
The unit used to measure the resistance is called ohm. In Eq. 16.2, if V=1 volt and I =1 ampere, the value of R would be 1 ohm. Thus a conductor would have a resistance of one ohm, if a current of one ampere passes through it when a potential difference of one volt is applied across it s ends. Ohm is usually represented by the greek letter
Example 16.2: the potential difference across an electric bulb is 220 V. if the current passing through it is 440mA, then find the resistance of the bulb. If the potential difference is increased to 250 V, what would be the value of current?
Solution:
Potential difference V=220V
Current I = 440 mA =440 A
Resistance R=?
By ohm’s law
Fig. 16.6 the resistance R of any wire is inversely proportional to its area A and is directly proportional to its length L.
Specific resistance
At a certain temperature the resistance of a conducting wire depends upon its length, area of crosssection and the nature of the material of the wire. By measuring the resistance of wires of different length and different area of cross section, it was found that:
- The resistance R of the wire is directly proportional to its length L. mathematically;
It means if the length of wire is doubled, its resistance will also be doubled and if its length is halved, then its resistance would become one half.
- The resistance R of the wire is inversely proportional to the area of cross-section A of the wire, i.e.,
It means that a thick wire would have smaller resistance than a thin wire.
After combining the above two ratios
Where is the constant of proportionality, known as specific resistance. Its value depends upon the nature of conductor i.e., copper, iron, tin and silver each would have a different values of .
In Eq. 16.3, if L = 1 m and A = then R = i.e., the resistance of one metre cube of a substance is equal to its specific resistance, according to Eq. 16.3 the unit of is ohm metre ( . the specific resistance of some metals is given in table 16.1.
Table 16.1
| Metal | Specific resistance |
| SilverCopperAluminiumTungstenplatinum | 1.621.692.755.2510.6 |
Example 16.3: length of a copper wire is 1 metre and its diameter is 2mmm. Find its resistance.
Solution:
Length of the wire = L= 1m
