If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be

Question

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

Smart Achievers · Accepted Answer

(3)

$R = \frac{ρ L}{π \frac{d^{2}}{4}}$

$\frac{∆ R}{R} = \frac{∆ L}{L} + \frac{2 ∆ d}{d}$

$\frac{∆ L}{L} = 0.1 %$ and $\frac{∆ d}{d} = 0.1 %$

$\frac{∆ R}{R} = 0.3 %$

Solution

Q.
If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

1 0.2%

2 0.144%

3 0.3%

4 0.1%

Ans.
(3)

   $R = \frac{ρ L}{π \frac{d^{2}}{4}}$

   $\frac{∆ R}{R} = \frac{∆ L}{L} + \frac{2 ∆ d}{d}$

   $\frac{∆ L}{L} = 0.1 %$ and $\frac{∆ d}{d} = 0.1 %$

$\frac{∆ R}{R} = 0.3 %$

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