The radius, length and resistance of a metal wire was measured in the laboratory as, The percentage error in resistivity of the material of the wire is

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Solution

Q.
The radius ( $r$ ), length ( $l$ ) and resistance ( $R$ ) of a metal wire was measured in the laboratory as [2024]

$r = (0.35 \pm 0.05) c m$

$R = (100 \pm 10) o h m$

$l = (15 \pm 0.2) c m$

The percentage error in resistivity of the material of the wire is

1 25.6%

2 39.9%

3 37.3%

4 35.6%

Ans.
(2)

   $\frac{∆ ρ}{ρ} = \frac{∆ R}{R} + 2 \frac{∆ r}{r} + \frac{∆ l}{l}$

   $= \frac{10}{100} + 2 \times \frac{0.05}{0.35} + \frac{0.2}{15}$

$= \frac{1}{10} + \frac{2}{7} + \frac{1}{75}$

   $\frac{∆ ρ}{ρ} = 39.9 %$

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