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

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 $4=\frac{2 \times 10^{-7} \times 2\pi \times 7 \times 10^{-2} \times n}{\pi\left(0.7 \times10^{-3}\right)^{2}}$
$\therefore n=70$