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## List the factors affecting the resistance of a conductor?

The electrical resistance of a conductor (or a wire) depends on the following factors :

- length of the conductor,
- area of cross-section of the conductor (or thickness of the conductor),
- nature of the material of the conductor, and
- temperature of the conductor.

We will now describe how the resistance depends on these factors.

### 1. Effect of Length of the Conductor

It has been found by experiments that on increasing the length of a wire, its resistance increases; and on decreasing the length of the wire, its resistance decreases. Actually, the resistance of a conductor is directly proportional to its length. That is,

Resistance, R ∝ l (where l is the length of conductor)

Since the resistance of a wire is directly proportional to its length, therefore, when the length of a wire is doubled, its resistance also gets doubled; and if the length of a wire is halved, then its resistance also gets halved. When we double the length of a wire, then this can be considered to be equivalent to two resistances joined in series, and their resultant resistance is the sum of the two resistances (which is double

the original value). From this discussion we conclude that a long wire (or long conductor) has more resistance, and a short wire has less resistance.

### 2. Effect of Area of Cross-Section of the Conductor

It has been found by experiments that the resistance of a conductor is inversely proportional to its area of cross-section. That is,

Resistance, R ∝ \(\frac{1}{A}\) (where A is area of cross-section of conductor)

Since the resistance of a wire (or conductor) is inversely proportional to its area of cross-section, therefore, when the area of cross-section of a wire is doubled, its resistance gets halved; and if the area of cross-section of wire is halved, then its resistance will get doubled. We know that a thick wire has a greater area of cross-section whereas a thin wire has a smaller area of cross-section.

This means that a thick wire has less resistance, and a thin wire has more resistance. A thick wire (having large area of cross-section) can be considered equivalent to a large number of thin wires connected in parallel. And we know that if we have two resistance wires connected in parallel, their resultant resistance is halved.

So, doubling the area of cross-section of a wire will, therefore, halve the resistance. From the above discussion it is clear that to make resistance wires (or resistors) :

- short length of a thick wire is used for getting low resistance, and
- long length of a thin wire is used for getting high resistance.

The thickness of a wire is usually represented by its diameter. It can be shown by calculations that the resistance of a wire is inversely proportional to the square of its diameter. Thus, when the diameter of a wire is doubled (made 2 times), its resistance becomes one-fourth (\(\frac{1}{4}\)), and if the diameter of the wire is halved (made \(\frac{1}{2}\)), then its resistance becomes four times (4 times).

Similarly, if the diameter of a wire is tripled (made 3 times), then its resistance will become \(\frac{1}{(3)^2}\) or \(\frac{1}{9}\) th of its original value.

### 3. Effect of the Nature of Material of the Conductor

The electrical resistance of a conductor (say, a wire) depends on the nature of the material of which it is made. Some materials have low resistance whereas others have high resistance. For example, if we take two similar wires, having equal lengths and diameters, of copper metal and nichrome alloy, we will find that the resistance of nichrome wire is about 60 times more than that of the copper wire. This shows that the resistance of a conductor depends on the nature of the material of the conductor.

### 4. Effect of Temperature

It has been found that the resistance of all pure metals increases on raising the temperature; and decreases on lowering the temperature. But the resistance of alloys like manganin, constantan and nichrome is almost unaffected by temperature.