Electric current does not flow freely in all materials. Every conductor offers some opposition to the flow of charges, which is called resistance. It depends on the length, area of cross-section, and nature of the material. To compare materials, we use a property called resistivity.
Resistance:
Resistance is the property of a conductor that opposes the flow of electric charges through it. It is represented as \(R\). Its SI unit is the \(ohm\), represented by the Greek letter omega (\(\Omega\)).
\(R\ =\ \frac{V}{I}\) or
\(I\ =\ \frac{V}{R}\)
It is obvious from the above equation that the current through a resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved.
One ohm:
If the potential difference across the two ends of a conductor is one volt and the current flowing through it is one ampere, then the resistance of the conductor is one ohm.
\(1\ ohm\ =\ \frac{1\ volt}{1\ ampere}\) or \(1\Omega\ =\ \frac{1V}{1A}\)
\(R\ \propto\ \frac{1}{A}\)
This means that a thicker wire (greater area) has lower resistance, while a thinner wire has higher resistance. A larger cross-sectional area provides more space for the movement of electrons, reducing opposition to current flow.
iii. Combined relation of resistance:
By combining the above two relations, we get:
\(R\ \propto\ \frac{l}{A}\)
Introducing a constant of proportionality called resistivity (\(\rho\)), we obtain:
\(R\ =\ \rho\ \frac{l}{A}\)
Resistivity:
Resistivity is a constant that depends on the nature of the material of the conductor. It is a characteristic property of a material and does not depend on its shape or size.
\(\rho\ =\ \frac{RA}{l}\)
SI unit of resistivity:
The SI unit of resistivity is ohm metre (\(\Omega\ m\))
Comparison of materials:
Metals and alloys generally have low resistivity, making them good conductors of electricity. Insulators like rubber and glass have very high resistivity and do not allow current to pass easily.
Tungsten is commonly used in electric bulb filaments due to its high melting point. Copper and aluminium are widely used in electrical transmission lines because they have low resistivity and allow current to flow easily with minimal energy loss.
Conductance:
The property of a material that helps the movement of charges and thus the current flow in the circuit is known as conductance. It is denoted as \(G\).
Mathematically, it is defined as the reciprocal of its resistance.
\(G\ =\ \frac{1}{R}\)
The SI unit of conductance of a material is \(ohm^{-1}\) or \(mho\) or \(siemen\)