Question

Find the resistance of the coil of length $l$, number of turns per unit length n, diameter of the wire d, radius of the coil R and resistivity $p$ ?

Answer 1

Total number of turns in the coil $N=nl$

Thus length of the wire used $L=N\left(2\pi R\right)=2\pi nlR$

Area of the cross-section of the wire $A=\frac{\pi d^2}{4}$

$\therefore$ Resistance of wire $R=\rho \frac{L}{A}=\frac{\rho \left(2\pi nlR\right)}{\pi d^2/4}=\frac{8nlR\rho }{d^2}$