Resistance

Resistance

The resistance of a conductor can be defined as the property of the conductor that opposes the flow of electric current through it. The SI unit of resistance is ohm. It is denoted by the upper case letter 'R'. When an electric current of 1 Ampere passes through a conductor, then the potential difference becomes 1 volt, this resistance of a conductor is known as 1Ω (ohm).
Metals like silver, copper, gold etc. have low resistance. Copper is used mostly in the wire as it offers low resistance. Some substances offer very high resistance. Some mostly used substances are given below with their composition, uses and resistance,

Factors affecting resistance

1. When we measure the resistance for two different lengths of wire having same cross section area, the resistance of the long wire is higher than short wire. The resistance of a conductor is directly proportional to its length. Longer the length of wire, greater will be the resistance. i.e. R∝ l
2. When we measure the resistance of two wire of the same length but different cross section area, we find thin wire has high resistance than the thicker one. The resistance of a conductor is inversely proportional to its cross- section area of the conductor. i.e. R∝ \(\frac{1}{A}\)
3. The resistance of the conductor also depends on its material which it is made of. Conductors of same length and size have different resistance if they are made of different materials.
4. The temperature also determines the resistance of the conductor.Resistance is directly proportional to the temperature of the conducting wire. The resistance of a conductor increases with increase in temperature.

Resistivity and conductivity

As we know that, the resistance of a conductor is directly proportional to its length and inversely proportional to its cross- sectional area. If 'l' is the length of a wire, 'A' is it's the cross- sectional area and 'R' is its resistance, then

R∝ l ........... (i)

R∝ \(\frac{1}{A}\) ................(ii)

From eq (i) and (ii) we have

R∝ \(\frac{l}{A}\)

∴ R =ρ \(\frac{l}{A}\)

Where,
ρ (Rho) = resistivity or specific resistance of the material
The SI unit of resistivity (ρ) is ohm- metre (Ωm).

If l = 1m, A = 1m², then R =ρ

ρ = R \(\frac{A}{l}\).

The resistivity of a material is numerically equal to the resistance of a conductor of unit area per unit length of a material.

The reciprocal of the resistivity (ρ) of a material is called its conductivity (σ) sigma.

Conductivity (σ) =\(\frac {1}{ resistivity (ρ)}\).