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Questions  

The specific resistance ρ of a thin wire of radius r=0.26±0.02cm, resistance R=(32±1)Ω and length l=78±0.01cm. Find the percentage error in ρ is

a
18%
b
20%
c
16%
d
22%

detailed solution

Correct option is A

Specific Resistance ρ=πr2Rl differentiate and divide with the same equation then multiply by 100 both sides  Δ ρρ×100=2Δ rr×100+Δ RR×100+Δ ll×100 Δ ρρ×100=[2×0.020.26+132+0.0178]×100 Δ ρρ×100=0.1538+0.03125+0.000128×100 percentage error in ρ=0.185 ×100=18%

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