The amount of heat produced in an electric ci | vedclass

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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 pro

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$6$

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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:$\frac{\Delta H}{H} = 2\left(\frac{\Delta I}{I}ight) + \frac{\Delta R}{R} + \frac{\Delta t}{t}.$Given percentage errors are $\frac{\Delta I}{I} 	imes 100 = 2\%,$ $\frac{\Delta R}{R} 	imes 100 = 1\%,$ and $\frac{\Delta t}{t} 	imes 100 = 1\%.$Substituting these values into the error equation:$\frac{\Delta H}{H} 	imes 100 = 2(2\%) + 1\% + 1\% = 4\% + 1\% + 1\% = 6\%.$Thus,the maximum possible error in the total heat produced is $6\%.$

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

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