Question

A wire of resistance $4\Omega$ is used to wind a coil of radius $7cm$. The wire has a diameter of $1.4mm$ 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

Answer: (D)

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 $4=\frac{2\times 10^{-7}\times 2\pi \times 7\times 10^{-2}\times n}{\pi {\left(0.7\times 10^{-3}\right)}^2}$
$\therefore n=70$