Question

List the factors on which the resistance of a wire depends.

Answer 1

Resistance

According to Ohm's law, the current passing through a conductor is directly proportional to the potential difference across this conductor.

Let $I$ be the current passing through the conductor and $V$ be the potential difference across the conductor, then their relationship can be expressed as,

$V\propto I$

According to the laws of proportionality,

$V=IR$

where $R$ is the constant of proportionality or the resistance.

Hence, resistance is the parameter that resists the flow of current inside a conductor.

The SI unit of resistance is ohm or $\Omega$.

Factors affecting resistance

1. As the length of the wire increases, the distance through which the current flows increases, and hence it experiences more resistance.
2. Therefore, resistance is directly proportional to the length of the wire, or $R\propto L$.
3. As the area of the wire increases, it allows the current to flow more efficiently, hence reducing its resistance.
4. Therefore resistance is inversely proportional to the area of the wire, or $R\propto \frac{1}{A}$.
5. Hence resistance can be written as, $R\propto \frac{L}{A}$.
6. According to the laws of proportionality,
7. $R=\rho \frac{L}{A}$
8. Where $\rho$ is called the resistivity of the wire.

Hence, the resistance of a wire mainly depends on the length and area of the wire.