a wire of radius r has resistances R. if is stretched to a wire of r/2 radius, then the resistance becomes
Correct answer: B. 4R
- A. 2R
- B. 4R
- C. 16R
- D. Zero
Explanation
Resistance of a wire is given by R = ρL/AWhere, ρ is resistivity of material of wire (constant)L is length of wireA is cross-sectional area of wireFor original wire: Area (A) = πr^2For stretched wire: Area (A') = π(r/2)^2 = πr^2/4Length (L) remains same for both wiresUsing the formula:Resistance of original wire = R = ρL/πr^2Resistance of stretched wire = R' = ρL/πr^2/4R'/R = πr^2/πr^2/4 = 4Therefore, the resistance of the stretched wire becomes 4 times the original resistance
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