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A wire of a given material has length '1' and resistance 'R'. Another wire of the same material having nine times the length and the same area of cross section will have a resistance equal to?

A3R

B1/9R

C1/3R

D9R

Answer:

D. 9R

Read Explanation:

  • Resistance is directly proportional to length and inversely proportional to area.

  • Let R be the resistance, l be the length, and A be the area of cross-section.

  • Then R = ρl/A, where ρ is the resistivity.

  • If the length becomes 9 times and the area remains the same, the new resistance R' will be:

  • R' = ρ(9l)/A = 9(ρl/A) = 9R


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