Question

the resistance of a wire of 0.01 cm radius is 10 Ω. if the resistivity of the material of the wire is $\sf{50 \times {10}^{ - 8}}$ Ω.m, find the length of the wire​

Answer 1

⇒ Given:

Radius of the wire = 0.01 cm

The resistance of the wire [R] = 10 Ω

Resistivity of the material used to make the wire [ρ] = $\sf{50\times10^8}$ Ω.m

⇒ To Find:

The length of the wire.

⇒ Solution:

It is given that the radius of the wire is 0.01 cm. To do the calculations, we need to convert it into the standard unit form, which is meter.

$\sf{\longrightarrow\:0.01\:cm=0.01\times10^{-2}\:m}$

Now, the formula we need to implement to find the answer is the formula of resistivity which is as given below:

$\sf{\implies\:R=\rho\dfrac{I}{A}}$

Simplifying the equation further:

$\sf{\longrightarrow\:R=\rho\dfrac{I}{\pi\:r^2}}$

Therefore, to find the length of the wire, we need to write the formula as:

$\sf{\longrightarrow\:I=\dfrac{R\pi\:r^2}{\rho}}$

Adding the values in the equation:

$\sf{\longrightarrow\:I=\dfrac{10\times3.14\times0.01\times10^{-2}\times0.01\times10^{-2}}{50\times10^{-8}}}$

$\sf{\longrightarrow\:I=\dfrac{31.4\times1\times10^-8}{50\times10^{-8}}}$

$\sf{\longrightarrow\:I=\dfrac{31.4}{50}}$

$\sf{\longrightarrow\:I=0.628\:m}$

The length of the wire is 0.628 m.

Answer 2

Explanation:

⇒ Given:

Radius of the wire = 0.01 cm

The resistance of the wire [R] = 10 Ω

Resistivity of the material used to make the wire [ρ] = \sf{50\times10^8}50×10

8

Ω.m

⇒ To Find:

The length of the wire.

⇒ Solution:

It is given that the radius of the wire is 0.01 cm. To do the calculations, we need to convert it into the standard unit form, which is meter.

\sf{\longrightarrow\:0.01\:cm=0.01\times10^{-2}\:m}⟶0.01cm=0.01×10

−2

m

Now, the formula we need to implement to find the answer is the formula of resistivity which is as given below:

\sf{\implies\:R=\rho\dfrac{I}{A}}⟹R=ρ

A

I

Simplifying the equation further:

\sf{\longrightarrow\:R=\rho\dfrac{I}{\pi\:r^2}}⟶R=ρ

πr

2

I

Therefore, to find the length of the wire, we need to write the formula as:

\sf{\longrightarrow\:I=\dfrac{R\pi\:r^2}{\rho}}⟶I=

ρ

Rπr

2

Adding the values in the equation:

\sf{\longrightarrow\:I=\dfrac{10\times3.14\times0.01\times10^{-2}\times0.01\times10^{-2}}{50\times10^{-8}}}⟶I=

50×10

−8

10×3.14×0.01×10

−2

×0.01×10

−2

\sf{\longrightarrow\:I=\dfrac{31.4\times1\times10^-8}{50\times10^{-8}}}⟶I=

50×10

−8

31.4×1×10

−

8

\sf{\longrightarrow\:I=\dfrac{31.4}{50}}⟶I=

50

31.4

\sf{\longrightarrow\:I=0.628\:m}⟶I=0.628m

The length of the wire is 0.628 m.