Question

Two resistances $100 \pm 5\,\Omega$ and $150 \pm 15\,\Omega$ are connected in series. If the errors are specified as standard deviations, the resultant error will be:

• A. $\pm 10\,\Omega$
• B. $\pm 10.6\,\Omega$
• C. $\pm 15.8\,\Omega$
• D. $\pm 20\,\Omega$

Hint:

When combining errors in series with standard deviations, use the root-sum-square formula: $\sqrt{e_1^2 + e_2^2}$.

Answer 1

The Correct Option is C

When standard deviations are given and components are added in series, the total error is calculated using the root-sum-square (RSS) method:
\[ \text{Resultant Error} = \sqrt{(5)^2 + (15)^2} = \sqrt{25 + 225} = \sqrt{250} \approx 15.8\,\Omega \]
This is because standard deviations (errors) are statistically independent and combine in quadrature rather than algebraically.