A wire of resistance 4 Ω is used to make a coil of radius 7 cm. The wire has a diameter of 1.4 mm and the resistivity of its material is $2 × 10^{-7}Ω m$. The number of turns in the coil will be

70

The correct answer is Option (1) → 70

Given:

Resistance, $R = 4\ \Omega$

Radius of coil, $r = 7\ \text{cm} = 0.07\ \text{m}$

Diameter of wire, $d = 1.4\ \text{mm} = 1.4 \times 10^{-3}\ \text{m}$

Resistivity, $\rho = 2 \times 10^{-7}\ \Omega\text{m}$

Area of cross-section of wire:

$A = \pi \left(\frac{d}{2}\right)^2 = \pi \left(0.7 \times 10^{-3}\right)^2 = 1.54 \times 10^{-6}\ \text{m}^2$

Length of wire (total):

$L = \frac{R A}{\rho} = \frac{4 \times 1.54 \times 10^{-6}}{2 \times 10^{-7}} = 30.8\ \text{m}$

Circumference of one turn:

$2\pi r = 2\pi \times 0.07 = 0.44\ \text{m}$

Number of turns:

$n = \frac{L}{2\pi r} = \frac{30.8}{0.44} = 70$

∴ The number of turns in the coil is $70$.