How many numbers of turns of nichrome wire of specific resistance 10^(-6) Ωm and diameter 2 mm that…

Q: How many numbers of turns of nichrome wire of specific resistance 10^(-6) Ωm and diameter 2 mm that should be wound on a cylinder of diameter 5 cm to obtain a resistance of 40 Ω ?

Sol. If R is the radius of the cylinder

r is the radius of the wire

N is the number of turns

$\large R’ = \rho \frac{l}{A}$

$\large R’ = \rho \frac{(2\pi R) N}{\pi r^2}$

$\large 40 = 10^{-6} \frac{(2 \times 2.5 \times 10^{-2}) N}{ 1 \times 10^{-6}}$

N = 800