Question

The masses of three copper wires are in the ratio 3 : 2 : 5 and their lengths are in the ratio 3 : 2 : 5. Then, the ratio of their electrical resistances is

• A. 1: 5: 15
• B. 3: 2: 5
• C. 3: 4: 5
• D. 5: 3: 2

Hint:

The resistance ratio depends on both the length and cross-sectional area, with mass and length related through the density and volume of the wire.

Answer 1

The Correct Option is A

The resistance \( R \) of a wire is given by \( R = \rho \frac{L}{A} \), where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area. Using the given ratios for mass and length, the resistance ratio is 1:5:15.