The resistance of a conductor depends on which of the following factors?
(A) Its length
(B) Its weight
(C) Its area of cross-section
(D) The nature of its material
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
The resistance of a conductor is given by \(R=\rho\frac{l}{A}\), where \(l\) is its length, \(A\) its area of cross-section and \(\rho\) the resistivity, a property of the material (it also changes with temperature).
(A) Its length Correct. Resistance is directly proportional to the length: a wire twice as long offers twice the resistance, because the current has to pass through more material.
(B) Its weight Incorrect. Weight does not appear in the formula. Two wires of the same material, length and thickness have the same resistance; a heavier wire differs only because its length or thickness differs.
(C) Its area of cross-section Correct. Resistance is inversely proportional to the area of cross-section: a thicker wire gives the current a wider path and so offers less resistance.
(D) The nature of its material Correct. The material decides the resistivity \(\rho\): copper and silver have a low resistivity, while nichrome has a high one and is used in heating elements.