Question

A metallic wire of uniform area of cross-section has a resistance $R,$ resistivity $ρ,$ and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity, and power rating at V volts are now denoted by $R'$, $ρ'$, and $P'$respectively. The corresponding values are correctly related as __________.
Fill in the blank with the correct answer from the options given below

• A. $ρ' = 2ρ, R' = 2R, P' = 2P$
• B. $ρ' = \frac{1}{2} ρ, R' = \frac{1}{2} R, P' = \frac{1}{2} P$
• C. $ρ' = ρ, R' = 16R, P' = \frac{1}{16} P$
• D. $ρ' = ρ, R' = \frac{1}{16} R, P' = 16P$

Answer 1

Answer: (C)

$ρ' = ρ, R' = 16R, P' = \frac{1}{16} P$

Answer 2

When the wire is stretched uniformly, the length increases, and the area decreases. The new resistance is proportional to the square of the change in length, which in this case leads to a 16-fold increase in resistance and a corresponding decrease in power.