Question

The error in the measurement of resistance, when \( (10 \pm 0.5) \) A current passing through it produces a potential difference of \( (100 \pm 6) \) V across it, is:

• A. \( 1\% \)
• B. \( 5.5\% \)
• C. \( 6.5\% \)
• D. \( 11\% \)

Hint:

The percentage error in a quotient \( R = V/I \) is the sum of the relative errors in \( V \) and \( I \). - Always express percentage errors as positive values.

Answer 1

The Correct Option is D

Step 1: Use the formula for percentage error
The resistance is given by: \[ R = \frac{V}{I}. \] The percentage error in resistance is given by: \[ \frac{\Delta R}{R} \times 100 = \left( \frac{\Delta V}{V} + \frac{\Delta I}{I} \right) \times 100. \] Step 2: Substitute values
\[ \frac{\Delta V}{V} = \frac{6}{100} = 6\%, \] \[ \frac{\Delta I}{I} = \frac{0.5}{10} = 5\%. \] \[ \text{Total percentage error} = 6\% + 5\% = 11\%. \] Thus, the correct answer is \( \boxed{11\%} \).