First slide

Accuracy; precision of instruments and errors in measurements

Question

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

Moderate

A

18%
B

20%
C

16%
D

22%

Solution

$S p e c i f i c R e s i s \tan c e ρ = \frac{π r^{2} R}{l} d i f f e r e n t i a t e a n d d i v i d e w i t h t h e s a m e e q u a t i o n t h e n m u l t i p l y b y 100 b o t h s i d e s$
$\frac{Δ ρ}{ρ} \times 100 = 2 \frac{Δ r}{r} \times 100 + \frac{Δ R}{R} \times 100 + \frac{Δ l}{l} \times 100 \frac{Δ ρ}{ρ} \times 100 = [\frac{2 \times 0.02}{0.26} + \frac{1}{32} + \frac{0.01}{78}] \times 100 \frac{Δ ρ}{ρ} \times 100 = [0.1538 + 0.03125 + 0.000128] \times 100 p e r c e n t a g e e r r o r i n ρ = 0.185 \times 100 = 18 %$

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