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A wire of resistance $4 \Omega$ is used to wind a coil of radius $7 \mathrm{~cm}$ . The wire has a diameter of $1.4 \mathrm{~mm}$ and the specific resistance of its $\mathrm{m}$ arterial is $\mathrm{2 \times 10^{-7} \Omega \mathrm{m}}$ . The number of turn in the coil is -
Option: 1
$50$

Option: 2
$40$

Option: 3
$60$

Option: 4
$70$

Answers (1)

best_answer

$\mathrm{l=2 \pi r \times n}$ $\leftarrow$ number of
$\uparrow$ circumference term

Use, $\mathrm{R=\frac{\rho l}{A} \Rightarrow 4 =\frac{2 \times 10^{-7} \times 2 \pi \times 7 \times 10^{-2} \times n}{\pi\left(0.7 \times 10^{-3}\right)^2} }$

$\mathrm{4 =\frac{14 \times 2 \times 10^{-9} \mathrm{n}}{0.49 \times 10^{-6}} }$

$\mathrm{2 =\frac{14 \times 10^{-9} . n \times 10^6}{0.49} }$

$\mathrm{0.98 =n \times 10^{-3} }$

$\mathrm{n =70}$

Hence option 4 is correct.

Posted by

Suraj Bhandari

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