A wire of given material having length l and area of cross-section 'A' has a resistance of 27 ohms. What would be the resistance of the same material having length l/3 and area of cross-section 3A?
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given:
length = l
area of cross-section = A
R = 27ohms
so, the formula is =
R = ∫×l/a......(i)
⇒ ∫ = R×a/l.....(ii) ( derived from i)
so, substituting values into equation (ii),
⇒∫ = 27A/l...(iii)
So, the given values of the new wire,
length = l/3
area of cross-section = 3A
∫ = 27A/l ( from iii)
So, new resistance,
R = 27A/l × l/3 × 1/3A
⇒R = 27/9
⇒R = 3ohms
∴ The resistance of the new wire is 3ohms.
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