(C) The formula for heat produced in an electric circuit is given by $H = I^2Rt.$To find the maximum relative error in $H,$ we use the formula for pro

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(C) The formula for heat produced in an electric circuit is given by $H = I^2Rt.$To find the maximum relative error in $H,$ we use the formula for propagation of errors:$\frac{\Delta H}{H} = 2\left(\frac{\Delta I}{I}\right) + \frac{\Delta R}{R} + \frac{\Delta t}{t}.$Given percentage errors are $\frac{\Delta I}{I} \times 100 = 2\%,$ $\frac{\Delta R}{R} \times 100 = 1\%,$ and $\frac{\Delta t}{t} \times 100 = 1\%.$Substituting these values into the error equation:$\frac{\Delta H}{H} \times 100 = 2(2\%) + 1\% + 1\% = 4\% + 1\% + 1\% = 6\%.$Thus,the maximum possible error in the total heat produced is $6\%.$

Class 11 Physics Units, Dimensions and Measurement Errors of Measurement

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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 ........... $\%$

AIEEE 2012 All AIEEE

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$1$
B
$2$
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$6$
D
$3$

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The percentage errors in the measurement of $p, q, r$ and $s$ are $1\%, 2\%, 3\%$ and $2\%$ respectively.
The percentage error in the measurement of $C$ will be . . . . . . $\%$.

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The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively,then find the maximum error in the measurement of the density of the cube.

MediumAIPMT 1996

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In five successive measurements, the mass of a ball is measured to be $2.61 \,g, 2.58 \,g, 2.40 \,g, 2.73 \,g$ and $2.80 \,g$. The mean absolute error in the measurement is (in $\,g$)

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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 ........... $\%$

Similar Questions

$A$ force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$,what is the maximum percentage error in pressure (in $\%$)?

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