error analysis

Question

The resistance R = V/I where V = (100 ± 5) V and I = (10 ± 0.2) A. What is the percentage error in R?

RankGuru · Accepted Answer

1. **Rule for Combination of Errors**: For a quotient $Z = A/B$, the relative error is the sum of relative errors: $\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}$.
2. **Error in Voltage ($V$)**:
   - $\% 	ext{ Error in } V = \frac{5}{100} 	imes 100 = 5\%$.
3. **Error in Current ($I$)**:
   - $\% 	ext{ Error in } I = \frac{0.2}{10} 	imes 100 = 2\%$.
4. **Summation**:
   - Total percentage error in $R = 5\% + 2\% = 7\%$.
5. **Result**: The uncertainty in resistance measurement is **7%**.

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