Directions: In the following questions, a statement of assertion (A) ...
The resistivity of the conductors is directly proportional to temperature.
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Directions: In the following questions, a statement of assertion (A) ...
Assertion: The resistivity of the conductor increases with increasing temperature.
Reason: The resistivity is the reciprocal of the conductivity.
The correct answer is option 'B' - Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
Explanation:
To understand the relationship between temperature and resistivity, we need to understand resistivity and conductivity first.
Resistivity:
Resistivity (ρ) is a property of a material that quantifies how strongly it resists the flow of electric current. It is denoted by the Greek letter rho (ρ) and is measured in ohm-meters (Ω·m). The resistivity of a material depends on its intrinsic properties and is a constant value for a given material.
Conductivity:
Conductivity (σ) is the reciprocal of resistivity and measures how easily a material can conduct electric current. It is denoted by the Greek letter sigma (σ) and is measured in siemens per meter (S/m). The conductivity of a material is also a constant value for a given material.
Relationship between Resistivity and Temperature:
The resistivity of a material generally increases with increasing temperature. This is because as the temperature increases, the atoms and molecules in the material vibrate more vigorously, leading to more frequent collisions with electrons. These collisions hinder the free flow of electrons, causing an increase in resistivity.
Relationship between Conductivity and Temperature:
The conductivity of a material generally decreases with increasing temperature. This is because as the temperature increases, the mobility of charge carriers (electrons or ions) decreases due to increased scattering caused by more frequent collisions with vibrating atoms and molecules. This decrease in mobility leads to a decrease in conductivity.
Explanation of the Assertion and Reason:
The assertion states that the resistivity of the conductor increases with increasing temperature, which is correct based on the relationship explained above. However, the reason given, which states that resistivity is the reciprocal of conductivity, is not the correct explanation for the assertion.
While it is true that resistivity (ρ) is the reciprocal of conductivity (σ), this fact alone does not explain why the resistivity increases with increasing temperature. The reason for this relationship lies in the increased collisions between charge carriers and vibrating atoms/molecules, which hinder the flow of current.
Therefore, both the assertion and reason are true, but the reason does not provide the correct explanation for the assertion. Hence, the correct answer is option 'B'.
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