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} R t$
$\therefore \frac{\Delta H}{H}=2$
$ \frac{\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}$
For maximum percentage error,
$\frac{\Delta H}{H} \times 100 =2$
$\frac{\Delta I}{I} \times 100+\frac{\Delta R}{R} \times 100+\frac{\Delta t}{t} \times 100$
$=2 \times 2 \%+1 \%+1 \%=6 \%$