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The heat generated in a circuit is given by $Q = I^{2} R t$ joule, where I is current, R is resistance and t is time . If the percentage errors in measuring I, R, t are 1%, 2%, 1% respectively. The maximum percentage error in meaning heat will be

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3 %

6 %

4 %

5 %

answer is A.

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Detailed Solution

$Q = I^{2} R t$
$\frac{Δ Q}{Q} \times 100 = 2 \times \frac{Δ I}{I} \times 100 + \frac{Δ R}{R} \times 100 + \frac{Δ t}{t} \times 100$
$\begin{array}{l} = 2 \times 1 % + 2 % + 1 % \\ = 5 % \end{array}$

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