Question

If the measured values of the voltage across and the current through a resistor are \((100 \pm 5)\,V\) and \((10 \pm 0.2)\,A\) respectively, then the error in the determination of the resistance is:

• A. 5%
• B. 7%
• C. 5.2%
• D. 9.6%

Hint:

Relative errors add when quantities are multiplied or divided.

Answer 1

The Correct Option is B

Resistance \(R = \frac{V}{I}\). Relative error in \(R\) is sum of relative errors in \(V\) and \(I\) (since division): \[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \] Given: \[ \frac{\Delta V}{V} = \frac{5}{100} = 0.05 = 5%, \frac{\Delta I}{I} = \frac{0.2}{10} = 0.02 = 2% \] So, \[ {Error in } R = 5% + 2% = 7% \]