The resistance of a wire is 5 Ω. Its new resistance in ohm, if stretched to 5 times of its original length will be :
Question
The resistance of a wire is 5 Ω. Its new resistance in ohm, if stretched to 5 times of its original length will be :
Solution
The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). This relationship is given by the formula:
R = ρ * (L / A)
where ρ (rho) is the resistivity of the material of the wire.
When a wire is stretched to 5 times its original length, its new length is 5L and its new cross-sectional area is A/5 (since the volume remains constant).
Substituting these values into the formula gives:
R_new = ρ * ((5L) / (A/5)) = ρ * (25L / A) = 25 * ρ * (L / A) = 25R
So, the new resistance of the wire will be 25 times its original resistance, which is 25 * 5 Ω = 125 Ω.
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