Which of the following statements are correct about the electrical resistance and resistivity of a wire? 1. Both quantities depend on the area of cross-section of the wire 2. Both depend on the temperature 3. Resistance of the wire is directly proportional to the resistivity of the wire 4. Resistivity of the wire is directly proportional to the length of the wire Select the correct answer using the code given below :
- A.1 and 2
- B.1 and 3
- C.2 and 3
- D.2 and 4
Correct answer
Explanation
The correct answer is C, 2 and 3. Both quantities change with temperature, and resistance is directly proportional to resistivity, while resistivity does not depend on the wire’s size.
Resistance is given by R = ρL/A, where ρ is the resistivity, L the length and A the area of cross-section. Resistance therefore grows with length and resistivity and falls as the wire gets thicker. Resistivity is a property of the material alone at a given temperature; copper has the same resistivity whether the wire is thick or thin, short or long. For metals both R and ρ rise as the temperature rises.
A is wrong because statement 1 is false: resistivity does not depend on the area of cross-section.
B is wrong for the same reason, as it includes statement 1.
D is wrong because statement 4 is false: resistivity does not depend on the length.
Exam tip: R = ρL/A; resistance depends on size and material, resistivity only on material and temperature (unit ohm-metre).
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