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Home > FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS

FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS - (Concept)

The resistance of a Conductor-

 The property of a conductor due to which it opposes the flow of current through it is called resistance. 

From Ohm's law, we can say that

The resistance of a conductor is numerically equal to the ratio of potential difference across its ends to the current flowing through it. 

$$
\text { Resistance }=\frac{\text { Potential difference }}{\text { Current }} \text { or } \quad R=\frac{V}{I}
$$


The SI unit of resistance is ohm which is denoted by the symbol omega, $(\Omega)$
Now, if the potential difference V is 1 volt and the current $I$ is 1 ampere, then resistance $R$ in the above equation becomes 1 ohm.

That is,

$$
1 \mathrm{ohm}=\frac{1 \text { volt }}{1 \text { ampere }}
$$
 

Resistance of the conductor depends on 

  • the length of the conductor. I.e A long wire (or conductor) has more resistance and a short wire has less resistance. 

  • The thickness of the conductor.  I.e a thick wire has less resistance whereas a thin wire has more resistance.

  • nature of the material of the conductor. 

  • the temperature of the conductor. I.e Rise in temperature of a wire (or conductor) increases its resistance.

 

From this dependency, we can say that 

 The resistance of a uniform metallic conductor is directly proportional to its length (L) and inversely proportional to the area of cross-section (A)

I.e

$$
\begin{aligned}
& \quad R \propto \text { land } \quad R \propto \frac{1}{A} \\
& \text { we get } \\
& R \propto \frac{l}{A} \\
& \text { or. } R=\rho \frac{l}{A}
\end{aligned}
$$

where $\rho$ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.

The SI unit of resistivity is $\Omega \mathrm{m}$. It is a characteristic property of the material.
Both the resistance and resistivity of a material vary with temperature.
Fact-
The metals and alloys have very low resistivity in the range of $10^{-8} \Omega \mathrm{~m}$ to $10^{-6} \Omega \mathrm{~m}$ . They are good conductors of electricity. Insulators like rubber and glass have a resistivity of the order of $10^{12} \Omega \mathrm{~m}$ to $10^{17} \Omega \mathrm{~m}$.
- Formula-

For a conductor of resistivity $\rho$ having a length of a conductor= I
and Area of a crosssection of conductor= A
Then the resistance of a conductor is given as

$$
R=\rho \frac{l}{A}
$$

Where $\rho \rightarrow$ Resistivity

Exam Chapter
JEE FOUNDATION Electricity
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