Question

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?

• A. 3R
• B. 1/9R
• C. 1/3R
• D. 9R

Answer 1

Answer:

D. 9R

• 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