Question

The heat emitted by a resistor is given by $H=I^{2}Rt$.
If the measured values are $I=\left(20\pm 1.5\right)A,R\left(200\pm 10\right)\Omega ,t=\left(10\pm 0.7\right)s$
Find the relative percentage and absolute error in the measurement of heat and also represent them in appropriate forms.

Answer 1

$\begin{array}{c}H=I^{2}Rt\\ error\%\frac{\Delta H}{H}=\left(\frac{2\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}\right)\times 100\\ =\left(\frac{2\times 1.5}{20}+\frac{10}{200}+\frac{0.7}{10}\right)\times 100\\ =15\%+5\%+7\%\\ =27\%\end{array}$
Now,
absolute value= measured value$-$actual value
$=1.5+10+0.7=12.2$