Question

two wire have their resistivities and diameters both in ratio 2:1 and lenghts in the ratio 5:1. The rario on their resitances is?

Answer 1

$\gamma1 \: be \: the \: resistivity \: of \: resistac \: 1$
$\gamma2 \: be \: the \: resistivity \: of \: resistac \: 2$

$\frac{ \gamma 1}{ \gamma 2} = \frac{2}{1}$

$\frac{l1}{l2} = \frac{5}{1} \: and \: \frac{d1}{d2} = \frac{2}{1}$

Using the formula from the above image we get,

$\frac{r1}{r2} = \frac{ \gamma1 }{ \gamma2 } \: \frac{l1}{l2} \: {\frac{d2}{d1} }^{2}$

Thus ratio of resistances will be,

$\frac{r1}{r2} \: = \frac{5}{2}$