The heat produced in a long wire is characterised by resistance,...

The heat produced in a long wire is characterised by resistance, current and time through which the current passes. If the errors in measuring these quantities are respectively

1 \%, 2 \%

and

1 \%

, then total error in calculating the energy produced is

Options

A $4 \%$
B $6 \%$
C $4 / 3 \%$
D $8 \%$

Correct answer

B. $6 \%$

Step-by-step solution

The heat produced in a wire due to current flow is given by

\begin{aligned}H & =I² R t \\ \therefore \frac{\Delta H}{H}& =\frac{2 \Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}\\ & =2 \times0.02+0.01+0.01=0.06=6 \% \end{aligned}

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