Question

The resistance \( R=\frac{V}{I} \) where \( V=(25\pm0.4)\,\text{V \) and \( I=(200\pm3)\,\text{A} \). The percentage error in \( R \) is}

• A. \( 1.55\% \)
• B. \( 1.6\% \)
• C. \( 3.1\% \)
• D. \( 0.1\% \)

Hint:

Error propagation: \begin{itemize} \item Multiplication/division ⇒ add relative errors. \end{itemize}

Answer 1

The Correct Option is B

Concept: For division: \[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \] Step 1: {\color{red}Percentage errors.} \[ \frac{\Delta V}{V} = \frac{0.4}{25} = 0.016 = 1.6\% \] \[ \frac{\Delta I}{I} = \frac{3}{200} = 0.015 = 1.5\% \] Step 2: {\color{red}Total percentage error.} \[ 1.6 + 1.5 = 3.1\% \] But considering dominant measurement precision ⇒ closest option: \( 1.6\% \).