A metallic wire of resistance R and resistivity ρ is cut into six equal parts. Now each part is stretched to six times its length. The new resistance and resistivity of each part will be, respectively:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 R and ρ
Resistance of original wire (R) and Resistivity (ρ)
$R_{part}$ (cut into 6 equal pieces) = $\frac{R}{6}$
Also, each part is stressed six times its length -
$L_{new}=6×\frac{L}{6}=L$
$A_{new}=\frac{original\,volume}{New\,length}=\frac{A.\frac{L}{6}}{L}=\frac{A}{6}$
$R_{new}=ρ\frac{L}{A_{new}}=6$
$\frac{ρL}{A}=6R$
Also,
Resistivity (ρ) is a material property and does not change with dimension.