Question

A coil contains N turns of insulated copper wire wound on to a cylindrical iron core of diameter D.
The copper wire has a diameter d. The resistivity of copper is ρ. Diameter D is much greater than
diameter d.
What is the total resistance between the two ends of the coil?

Answer 1

Final Answer : Total Resistance between two ends of combination : 4pDN/d^2

Steps and Understanding :
1) Diameter of copper wire, d
Diameter of Cylindrical Iron one : D.
No. of turns : N

Since, D>>d
Length of copper wire ,
L = No. of turns * Circumference of cylinder
= N * (πD)
= NπD

Area of cross section of copper wire,
$a = \frac{\pi {d}^{2} }{4}$

2) Now,
Resistance between two ends of combination
is
=> pL/A
=> p * NπD / (πd^2/4)
=> 4pDN/d^2