Question

The amount of heat produced in an electric circuit depends upon the current $(I)$, resistance $(R)$ and time (t). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be

• A. $1\%$
• B. $2\%$
• C. $6\%$
• D. $3\%$

Answer 1

Answer: (C)

Given $:\frac{\Delta I}{I}\times 100=2\%;$
$\frac{\Delta R}{R}\times 100=1\%$ and $\frac{\Delta t}{t}\times 100=1\%$
Heat produced, $H=I^{2}Rt$
Maximum possible error in heat produced,
$=\frac{\Delta H}{H}\times 100$
$=2\left(\frac{\Delta I}{I}\times 100\right)+\frac{\Delta R}{R}\times 100+\frac{\Delta t}{t}\times 100$
$=2\times 2\%+1\%+1\%=6\%$