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Which of the following statement is correct for the resistance of pure metal and its alloy if the length and the cross-sectional area is same:
1. Resistance of pure metal will always be greater than its alloy
2. Resistance of pure metal will always be less than its alloy
3. Resistance of pure metal will always be equal to its alloy
4. Can't say

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Correct Answer - Option 2 : Resistance of pure metal will always be less than its alloy

CONCEPT:

  • Resistivity (ρ): The property of a conductor that opposes the flow of electric current through them and independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.
    • The unit for resistivity is the ohm-meter (Ω-m).
    • The resistivity of a material depends on its nature and the temperature of the conductor.
    • The resistivity of a material doesn't depend on its shape and size (length and area).
  • Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.
    • It is denoted by R and the SI unit is the ohm (Ω).
  • The resistance is given by:

\(⇒ R=\frac{ρ l}{A}\)

Where ρ = resistivity, l = length, and A = cross-sectional area

EXPLANATION:

  • The resistance of a conductor is given as,

\(⇒ R=\frac{ρ l}{A}\)

If l and A is not changing,

⇒ R ∝ ρ     ----(1)

  • By equation 1 it is clear that the resistance is proportional to resistivity.
  • We know that the resistivity of an alloy is much higher than those of pure metal. So the resistance of pure metal will always be less than its alloy. Hence, option 2 is correct.

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