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Resistance

The property of substance by virtue of which it opposes the flow of current through it is known as the resistance.

Formula of resistance

For a conductor if l = length of a conductor A = area of cross-section of conductor, n = number of free electrons per unit volume in conductor, τ = relaxation time, then resistance of conductor,

where ρ = resistivity of the material of conductor.

Unit and dimension Its SI unit is V/A or (Ω). Also 1 ohm = 109 emu of resistance. Its dimension is [ML2 T–3A–2].

Dependence of resistance

The resistance of a conductor depends upon the following factors:
• Length of the conductor: Resistance of a conductor is directly proportional to its length, i.e., R  l and inversely proportional to its area of cross section, i.e., R  1/A.
• Temperature: For a conductor, Resistance  temperature
If R0 = resistance of conductor at 0°C
Rt = resistance of conductor at t°C
and α, β = temperature co-efficient of resistance
then Rt = R0 (1 + αt + βt2) for t > 300°C and Rt = R0 (1 + αt) for t ≤ 300°C or

If R1 and R2 are the resistances at t1°C and t2°C, respectively, then .

The value of α is different at different temperature. Temperature coefficient of resistance averaged over the temperature range t1°C to t2°C is given by which gives R2 = R1[1 + α (t2t1)]. This formula gives an approximate value.