P27_017.PDF

17. The resistance of the coil is given by R = ρL/A ,where L is the length of the wire, ρ is the resistivity

of copper, and A is the cross-sectional area of the wire. Since each turn of wire has length 2 πr ,where

r is the radius of the coil, then L = (250)2 πr = (250)(2 π )(0 . 12 m) = 188 . 5m. If r w is the radius of the

wire itself, then its cross-sectional area is A = πr w = π (0 . 65

10 − 3 m) 2 =1 . 33

10 − 6 m 2 . According to

Table 27-1, the resistivity of copper is 1 . 69

10 − 8 Ω

m. Thus,

A = (1 . 69

10 − 8 Ω

m)(188 . 5m)

=2 . 4Ω .

1 . 33

10 − 6 m 2

R = ρL