Answer to Question #138033 in Electric Circuits for Austin

Question

A coil of annealed copper wire has 820 turns, the average length of which is 9 inches. If the diameter of the wire is 32 miles, calculate the total resistance of the coil at 20°C.

Answer 1

So the resistance is equal to $R =\frac {p\times l} {S}$ , where $p$ is the resistivity of the circuit, and $S$ is the cross-sectional area, i.e. $p = 0. 0172\frac {Ω × mm ^ 2} {m}$ , the wire length is equal to $l = N\times L$ , where $N$ is the number of turns, and $L$ is the length of one turn, then$l = 820\times 0.23 = 188.6 m$

$S=\pi \times \frac {d^2} 4= \pi \times \frac {51499.01^2}{4}= 2 082 992 192.59 m^2$ $= 2 082 992 192.59 \times 10^6 mm^2$ .

$R=\frac{0.0172\times 188.6}{ 2 082 992 192.59 \times 10^6 }$$=1.56 \times 10^{-15} \Omega$ .