A metallic wire of uniform area of cross section has a resistance R, resistivity $\rho$ 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', $\rho'$ and P' respectively corresponding values are correctly related as __________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
Resistivity is independent of geometrical parameter.
$\Rightarrow \rho' = \rho$
If radius is reduced to half then its area will be reduced by 4 times. Since volume is constant its length becomes 4 times.
$\Rightarrow R' = \frac{\rho' l'}{A'} = 16 R$
$ P = \frac{V^2}{R} \Rightarrow P' = \frac{V^2}{16R} = \frac{P}{16}$
The correct answer is Option (3) → $\rho'=\rho, R'=16 R, P'=(1 / 16) P$