Q. If voltage $V = (100\ \pm 5)$ volt and current $I = (10\ \pm 0.2)\ A,$ the percentage error in resistance $R$ is

A) 5.2%
B) 25%
C) 7%
D) 10%
Explanation

Given, voltage $V = (100 \pm 5)\ volt,$ Current $I = (10 \pm 0.2)A$ From Ohm’s law $V = IR$ $\therefore\ \ \ \ \ \ \ Resistance\ R = \frac{V}{I}$ Maximum percentage error in resistance $\left( \frac{\mathrm{\Delta}R}{R} \times 100 \right) = \left( \frac{\mathrm{\Delta}V}{V} \times 100 \right) + \left( \frac{\mathrm{\Delta}I}{I} \times 100 \right)$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left( \frac{5}{100} \times 100 \right) + \left( \frac{0.2}{10} \times 100 \right)$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 5 + 2 = 7\%$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.