Question

A cylindrical copper rod has length L and resistance R. If it is melted and formed into another rod of length 2L. the resistance will be

• A. R
• B. 2R
• C. 4R
• D. 8R

Answer 1

Answer: (C)

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made.The resistance of a wire can be expressed as $R=\rho \frac{L}{A}$,
where,
$\rho$ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity
L - Length of the conductor
A - Area of cross section of the conductor.
From this relation, we observe that the length is directly proportional to the resistance and the area of cross section is inversely proportional to the resistance.
In this case, the length of the conductor is doubled (2L) and so the resistance will be 2R. Now when the length is doubled the area of cross section is halved. S0, the resistance will decrease again by a factor of 2.
Hence, the new resistance of the wire will be $R^{\prime }=\rho \frac{2L}{A/2}$ = 4($\rho \frac{L}{A}$) = 4R.