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Home Q & A Board Science-Related Homework Help Physics
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ogr8dane ogr8dane
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11 years ago
The resistance of a certain wire is 11 ohms.

(a) What would the resistance of the same wire be if it were three times as long?

(b) If it had three times the diameter?
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3 Replies
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#1
11 years ago
a) 33 ohms

b) 11/9 ohms

See the Wikipedia article. Right underneath "Resistance of a conductor" it has a formula for the resistance of a wire/conductor. For A simply multiply l by 3, so then R is multiplied by 3 as well, so you get 33 ohms.
For B you have to determine that the area, A, equals pi*r^2. So if the diameter is tripled, the radius is tripled. And in the formula for area, that means it will now be pi*(3r)^2, so you get 9pi*r^2 on the denominator.
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onefallinstaronefallinstar
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#2
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11 years ago
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#3
11 years ago
(a) By R = rho x A/L
=>11 = rho x A/L --------------(i)
2nd case:-
R' = rho x A/3L = 1/3 x [rho x A/L] = 1/3 x 11 = 3.67 ohm
(b)  By R = rho x A/L
=>11 = rho x A/L
=>11 = rho x {pi x d^2/4L} --------------(i)
2nd case:-
R' = rho x A'/L = rho x {pi x 9d^2/4L} = 9 x [rho x {pi x d^2/4L}] = 9 x 11 = 99 ohm
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