Question

The resistance of a wire of 0.01 cm radius is 10 ohm. If the resistivity of the material of
the wire is 50 x 10^-8 ohm meter, find the length of the wire.
(2015)​

Answer 1

$\fbox{\texttt{\green{Answer:}}}$

Length (l) of the wire = 62.86 cm

$\fbox{\texttt{\pink{Given:}}}$

Resistance (R) = $\bold{10\Omega}$

Resistivity ($\bold{\rho)=50\times{10^{-8}}\Omega\:m}$

Radius (r) = $\bold{0.01\:cm=0.01\times{10^{-2}}\:m}$

$\fbox{\texttt{\blue{To\:find:}}}$

Length (l) of the wire.

$\fbox{\texttt{\orange{Formula\:used:}}}$

$\bold{R=\rho\frac{l}{A}}$

$\fbox{\texttt{\red{How\:to\:Find:}}}$

Area (of the wire) = $\bold{\pi\:r^2=}$

$\bold{\frac{22}{7}\times{}(0.01\times{}10^{-2})^2=}$

$\bold{3.143\times{}10^{-4}\:m^2}$

Now, $\bold{R=\rho\frac{l}{A}}$

$\implies\bold{l=\frac{R\times{A}}{\rho}}$

Substituting the respective values, we get :-

$\implies\bold{l=\frac{10\times{}3.143\times{}10^{-4}}{50\times{}10^{-8}}}$

$\implies\bold{l=0.6286\:m=62.86\:cm}$

Answer 2

$\bold\green{\underline{Given}}$

• The resistance of wire=0.01cm=0.01*10^-2
• Radius of wire R=10 ohm
• The resistivity of wire P=50*10^-8

$\bold\green{\underline{Find=>Length}}$

• by using formula here

⟹R=P*l/πr²

⟹l=Rπr²/P

⟹l=10*3.14*0.01*10^-2*0.01*10^-2/50*10^-8

⟹l=314*10^-4/50*10^-8*10^5

⟹l=6.28*10^-4/10^-3

⟹l=0.628m

Hence,

$\bold\green{\underline{Length\:of\:wire=>0.628m}}$