Question

According to Joule's law of heating, the heat produced is given by $H=I^{2}Rt,$ where $I$ is current, $R$ is resistance and $t$ is the time. If the errors in the measurement of $I,R$ and $t$ are $3\%$, $4\%$ and $6\%$ respectively, then the error in measurement of $H$ is:

• A. $17\%$
• B. $8\%$
• C. $16\%$
• D. $25\%$

Answer 1

The correct option is C $16\%$

From the given formula
$H=I^{2}Rt$
We can write that,
$\frac{\Delta H}{H}=\frac{2\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}$
For percentage error
$\frac{\Delta H}{H}\times 100=(\frac{2\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t})\times 100$
From the data given in the question,
$\%$ error in measurement of heat produced
$\frac{\Delta H}{H}\times 100=(2\times 3)+4+6=16\%$
Thus, option (c) is the correct answer.