1. The resistance of a metal wire is R units. Its diameter is d m and its length is l m. It is known that R varies inversely as the square of d and directly as l. When the length of a metal wire is 10m and its diameter is 4mm, its resistance is 75 units.
a) Express R in terms of d and l.
b) Find the resistance of a metal wire of length 40m and diameter 1cm.
Variation
2011-02-19 4:31 pm
回答 (1)
2011-02-19 8:11 pm
✔ 最佳答案
a)Let k = constant of proportionality
R = resistance = 75 unit
l = length (m) = 10 m
d = diameter (m) = 0.004 m
R = kl/d^2
k = Rd^2/l
k = 75 (0.004)^2/10 = 0.00012
R = (0.00012) l/d^2
b)
l = 40 m
d = 1 cm = 0.01 m
R = (0.00012)l/d^2
R = (0.00012) (40)/(0.01)^2
R = 0.0048/0.0001
R = 48 unit
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