Q. According to $Joule^{'}s$ law of heating, heat produced $H = I^{2}Rt,$ where $I\$is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I,R$ and $t$ are 3%, 4% and 6% respectively then error in the measurement of $H\$is
A) $\pm 17\%$
B) $\pm 16\%$
C) $\pm 19\%$
D) $\pm 25\%$
Explanation
$H = I^{2}Rt$ $\therefore\frac{\mathrm{\Delta}H}{H} \times 100 = \left( \frac{2\mathrm{\Delta}I}{I} + \frac{\mathrm{\Delta}R}{R} + \frac{\mathrm{\Delta}t}{t} \right) \times 100$ $= (2 \times 3 + 4 + 6)\% = 16\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.