Directions: In the following questions, a statement of assertion (A) ...
P is the characteristic of. the material of resistors. It does not depend on the length and cross-sectional area of resistors. But R depends on the length and the cross-sectional area of the resistor. So, R1 may be greater than R2 even when pi ≤ p 2.
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Directions: In the following questions, a statement of assertion (A) ...
Assertion: If p1 and p2 are the resistivity of the materials of two resistors of resistances R1 and R2 respectively and R1 > R2.
Reason: The resistance R = p l/A ⇒ p1 > p2 if R1 > R2.
The given assertion and reason are related to the concept of resistivity and resistance. Let's understand them in detail:
Resistivity:
- Resistivity is a property of a material that defines how strongly it opposes the flow of electric current.
- It is denoted by the symbol p and its SI unit is ohm-meter (Ω·m).
Resistance:
- Resistance is a measure of the opposition to the flow of electric current in a circuit component.
- It is denoted by the symbol R and its SI unit is ohm (Ω).
- The resistance of a conductor depends on its resistivity, length, and cross-sectional area.
Explanation:
- The resistance of a conductor is given by the formula R = (p * l) / A, where p is the resistivity, l is the length, and A is the cross-sectional area of the conductor.
- From the given assertion, R1 > R2, which means the resistance of the first resistor is greater than the resistance of the second resistor.
- The reason states that p1 > p2 if R1 > R2. This can be understood by rearranging the resistance formula as p = (R * A) / l. If R1 > R2, it implies that the cross-sectional area (A) and length (l) are the same for both resistors. Therefore, p1 > p2.
Conclusion:
- Both the assertion and reason are true.
- The reason correctly explains the assertion, as the resistivity of a material determines its resistance when the length and cross-sectional area are constant.
- Therefore, option 'A' is the correct answer.
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