Question

answer koe tou bata do​

Answer 1

Solution :

Given :-

Diameter of wire = 0.5mm

Resistivity of wire = 1.6×10$^{-5}$ Ωm

Resistance of wire = 10Ω

To Find :-

▪ Length of wire

▪ Change in resistance, if the diameter is doubled

Concept :-

Resistivity is the materialistic property of conductor. It doesn't depend upon length and area of conductor.

Formula of resistance in terms of resistivity, length of wire and cross section of wire is given by...

$\underline{\boxed{\bf{\pink{R=\rho\dfrac{l}{A}}}}}$

Calculation :-

$\implies\sf\:R=\rho\dfrac{l}{\pi{r}^2}\\ \\ \implies\sf\:10\pi=1.6\times 10^{-5}\times \dfrac{l}{(0.25\times 10^{-3})^2}\\ \\ \implies\sf\:l=\dfrac{10\pi\times (0.25\times 10^{-3})^2}{1.6\times 10^{-5}}\\ \\ \implies\sf\:l=\dfrac{0.196\times 10^{-5}}{1.6\times 10^{-5}}\\ \\ \implies\boxed{\bf{\orange{l=0.12\:m}}}\\ \\ \mapsto\sf\red{R\propto\dfrac{1}{r^2}}\\ \\ \mapsto\sf\:\dfrac{R_1}{R_2}=\dfrac{{r_2}^2}{{r_1}^2}\\ \\ \mapsto\sf\:\dfrac{R_1}{R_2}=(2)^2\\ \\ \mapsto\boxed{\bf{\purple{R_2=\dfrac{R_1}{4}}}}$

Answer 2

$\large\underline{ \underline{ \green{ \bold{Answer}}}}$

length of wire = 1227.6m

Resistance = 2.5ohm

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⠀⠀⠀$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanA{\green{TiOn }}}}}}}}$

$\large\underline{ \underline{ \color{red}{ \bold {Given}}}}$

➥ ⠀ Diameter = 0.5mm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=0.5×10-³m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 5 × 10-⁴m

➥⠀⠀Resistivity (p) = 1.6 × 10^-8 ohm meter.

$\large\underline{ \underline{ \red{ \bold {To \:Find}}}}$

we need to find the length of the wire.

⠀⠀⠀$\huge\underline{ \mathrm{ \color{green}{Solu{\pink{tiOn}}}}}$

➥⠀⠀⠀${\underline{\boxed{\color{blue}{\bf{R=\frac{pl}{A}}}}}}$

⠀⠀${\underline{\boxed{\color{blue}{\bf{R=\frac{pl}{\pi{d}^{2}/4}}}}}}$⠀⠀⠀ [A= πd²/4]

so,⠀⠀⠀⠀⠀⠀⠀l= Rπd²/4p

➜⠀⠀⠀$\bf\: = \frac{10}{4} \times \frac{22}{7} \times \frac{(5 \times 10 {}^{ - 4} ) {}^{2} }{1.6 \times {10}^{ - 8} }$

➜⠀⠀⠀$\bf\:l = \frac{220}{8} \times \frac{25}{1.6}$

➜⠀⠀⠀$\bf\:l = 122.76m$

If the diameter of wire is doubled then the resistance will become ¼th of the original resistance.

since ,

⠀⠀⠀⠀⠀⠀⠀⠀R ∝ 1/A

⠀⠀⠀⠀⠀⠀now restance R/4

⠀⠀⠀⠀⠀⠀⠀⠀ = 10/4

⠀⠀⠀⠀⠀⠀⠀⠀${\underline{\boxed{\color{blue}{\bf{R=2.5m}}}}}$

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