Question

Find the radius of the wire of length $25m$ needed to prepare a coil of resistence $25\Omega$ (Resistivity of material of wire is $3.142\times {10}^{-7}\Omega m$)

Answer 1

We know that

$R=\rho \frac{l}{4}$

HEre, $R=25\Omega$, $\rho =3.142\times {10}^{-7}\Omega m$

$A=\pi r^2$, $l=25m$

$r$ is the radius of circular cross ectional of wire. So,

$\Rightarrow$ $25=(3.142\times {10}^{-7})\frac{\left(25\right)}{\left(3.142\right)r^2}$

$\Rightarrow$ $r^2{10}^{-7}$

$\Rightarrow$ $r={10}^{-\frac{7}{2}}=3.16\times {10}^{-3}m$

Radius of cross section is $3.16mm$