Question

The heat dissipated in a resistor can be obtained by the measurement of resistance, current and time. If the maximum error in the measurement of these quantities is $1\%,2\%$ and $1\%$ respectively, the maximum error in the determination of the dissipated heat is

• A. $4\%$
• B. $6\%$
• C. $\frac{4}{3}\%$
• D. $2\%$

Answer 1

Answer: (B)

Heat dissipated in a resistor is given by
$H=I^{2}Rt$
$\therefore \frac{\Delta H}{H}=2$
$\frac{\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}$
For maximum percentage error,
$\frac{\Delta H}{H}\times 100=2$
$\frac{\Delta I}{I}\times 100+\frac{\Delta R}{R}\times 100+\frac{\Delta t}{t}\times 100$
$=2\times 2\%+1\%+1\%=6\%$