Mathematics In Physics Question 6
Question 6 - 2024 (31 Jan Shift 1)
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:
(1) $0.2 %$
(2) $0.3 %$
(3) $0.1 %$
(4) $0.144 %$
Show Answer
Answer: (2)
Solution:
$\mathrm{R}=\frac{\rho \mathrm{L}}{\pi \frac{\mathrm{d}^{2}}{4}}$
$\frac{\Delta \mathrm{R}}{\mathrm{R}}=\frac{\Delta \mathrm{L}}{\mathrm{L}}+\frac{2 \Delta \mathrm{d}}{\mathrm{d}}$
$\frac{\Delta \mathrm{L}}{\mathrm{L}}=0.1 %$ and $\frac{\Delta \mathrm{d}}{\mathrm{d}}=0.1 %$
$\frac{\Delta \mathrm{R}}{\mathrm{R}}=0.3 %$
