Class 10 > Unit # 15: Current Electricity > Resistance & Resistivity

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Electric Resistance and Factors Affecting Resistance

Q.4 Define Resistance. Also describe factors on which resistance depends.

Resistance

"The ratio of the potential difference applied across the ends of a conductor to the current passing through it is known as the resistance of that conductor."

Mathematically, electric resistance ($R$) is expressed as:

$R = \frac{V}{I}$

S.I. Unit of Resistance

The SI unit of resistance is the Ohm ($\Omega$).

Definition of One Ohm ($\Omega$): One ohm is the resistance of a conductor through which a current of $1\text{ A}$ (ampere) passes when a potential difference of $1\text{ V}$ (volt) is maintained across the ends of the conductor.

Factors on Which Resistance Depends

The electrical resistance of a metallic conductor depends upon the following physical factors:

1. Length ($L$): The resistance $R$ of a conductor is directly proportional to its length ($L$). Longer wires offer more resistance to the flow of charge.
2. Cross-Sectional Area ($A$): The resistance $R$ is inversely proportional to the cross-sectional area ($A$) of the conductor. Thicker wires offer less resistance.
3. Nature of Material: The resistance depends on the atomic structure and material composition of the conductor.
4. Temperature: Resistance increases with an increase in temperature for metallic conductors.

Mathematical Derivation

$R \propto L \quad \text{--- (i)}$
$R \propto \frac{1}{A} \quad \text{--- (ii)}$

Combining relations (i) and (ii):

$R \propto \frac{L}{A}$
$R = \rho \frac{L}{A}$

Where $\rho$ (rho) is a constant of proportionality known as resistivity or specific resistance of the material.

Rearranging the formula for resistivity ($\rho$):

$\rho = \frac{R \cdot A}{L}$

Unit of Resistivity

The SI unit of resistivity is ohm-meter ($\Omega\cdot\text{m}$), derived as follows:

$\text{Unit of } \rho = \frac{\Omega \cdot \text{m}^2}{\text{m}} = \Omega\cdot\text{m}$

Fig: Illustration of how conductor length ($L$) and cross-sectional area ($A$) affect electrical resistance.

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