A wire with a resistance of 6 Ω is drawn out through a die so that its new length is three times its
Source: JAMB · 2023
A wire with a resistance of 6 Ω is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.
Explanation
The volume of the wire stays the same. If the length becomes 3 times, the cross-sectional area becomes one third.
R = ρl/A, so the resistance rises by 3 × 3 = 9 times.
New resistance = 6 × 9 = 54 Ω.
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