Question

A wire of resistance $4\Omega$ is used to wind a coil of radius $7$cm. The wire has a diameter of $1.4$mm and the specific resistance of its material is $2\times {10}^{-7}\Omega$m. The number of turns in the coil is?

• A. $50$
• B. $40$
• C. $60$
• D. $70$

Answer 1

The correct option is D $70$

Let n be the number of turns in the coil, Then total length of wire used,
$l=2\pi r\times n=2\pi \times 7\times {10}^{-2}\times n$
Total resistance, $R=\rho \frac{l}{A}$
or $4=\frac{2\times {10}^{-7}\times 2\pi \times 7\times {10}^{-2}\times n}{\pi (0.7\times {10}^{-3}{)}^2}$
$\therefore n=70$.