A wire of length 1 m has a resistance of 2 ohms. Obtain the resistance if specificresistance is double, the diameter is double and the length is made three times the first
Question
A wire of length 1 m has a resistance of 2 ohms. Obtain the resistance if specificresistance is double, the diameter is double and the length is made three times the first
Solution
The resistance (R) of a wire is given by the formula:
R = ρL/A
where: ρ is the resistivity or specific resistance of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
The cross-sectional area (A) of a wire with diameter (d) is given by the formula:
A = π(d/2)^2
Given that the specific resistance is doubled, the diameter is doubled, and the length is tripled, we can substitute these changes into the formulas.
The new resistivity (ρ') is 2ρ. The new length (L') is 3L. The new diameter (d') is 2d, so the new area (A') is π((2d)/2)^2 = πd^2 = 4A.
Substituting these into the resistance formula gives:
R' = ρ'L'/A' = 2ρ * 3L / 4A = 6ρL / 4A = 1.5 * ρL / A = 1.5 * R
So the new resistance is 1.5 times the original resistance. If the original resistance was 2 ohms, the new resistance is 1.5 * 2 = 3 ohms.
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