Question

The resistance of a wire of uniform diameter $D$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2D$ and length $4L$ will be :

• A. $2R$
• B. $R$
• C. $R/2$
• D. $R/4$

Answer 1

The correct option is B $R$

Given $R=\frac{pL}{{\left(\frac{\pi D^2}{4}\right)}^2}$ ------------ (1)
Resistance of second wire

$R^1=\frac{p4L}{{\left(\frac{\pi (2D{)}^2}{4}\right)}^2}$

$=\frac{p4L}{4\left(\frac{\pi D^2}{4}\right)}$

$R^1=\frac{pL}{\frac{\pi D^2}{4}}$
From ( 1 ) $R^1=R$