Question

A metallic wire has a resistance of $1\Omega$. A second wire of the same material of double the length and half of the radius of the first wire will have a resistance of _____.

• A. $4\Omega$
• B. $8\Omega$
• C. $10\Omega$
• D. $20\Omega$

Answer 1

The correct option is B $8\Omega$

For the first wire, $R_1=\frac{\rho l}{\pi r^2}=1\Omega$
For the second Wire, $R_2=\frac{\rho \left(2l\right)}{\pi (\frac{r}{2}{)}^2}=\frac{8\rho l}{\pi r^2}=9R_1=8\Omega$