Question

Q5.There is a wire of length l and cross section A. Which of the following have least Resistance? 4 points (a)Length doubled, Area halved (b)Length tripled, Area doubled (c)Length halved, Area doubled (d)The original Wire

Answer 1

Answer:

option c is correct.

Explanation:

Answer 2

When the length will be halved and the area will be doubled, then the wire will have the least resistance. (Option-C)

• If a wire is made up of a material having resistivity rho, length L, and area of cross-section A, then its resistance R is represented as R = (rho)×L/A.
• In option 1, the length of the wire is doubled and the area of its cross-section is halved. Thus, the resultant resistance becomes 4 times the initial, that is 4 × (rho)×L/A.
• In option 2, the length of the wire is tripled and the area of its cross-section is doubled. Thus, the resultant resistance becomes 3/2 times the initial, that is 3/2 × (rho)×L/A.
• In option 3, the length of the wire is halved and the area of its cross-section is doubled. Thus, the resultant resistance becomes 1/4 times the initial, that is 1/4 × (rho)×L/A.
• In option 4, the length and the area of the cross-section of the wire are the same as the initial. Thus, the resultant resistance is equal to the initial, that is (rho)×L/A.
• On comparing all the given options, we get the lowest resistance is 1/4 times the initial, that is 1/4 × (rho)×L/A.
• That's why when the length will be halved and the area will be doubled, then the wire will have the least resistance.