Mathematics in Physics

JEE Main level, single correct, medium

116 of 121

Question 116 of 121

The amount of heat produced in an electric circuit depends upon the current (I)(I), resistance (R)(R) and time (t)(t). If the error made in the measurements of the above quantities are 2%,1%2 \%, 1 \% and 1%1 \% respectively then the maximum possible error in the total heat produced will be

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Answer: (C) 6%6 \%

Given : ΔII×100=2%\frac{\Delta I}{I} \times 100=2 \%;
ΔRR×100=1%\frac{\Delta R}{R} \times 100=1 \% and Δtt×100=1%\frac{\Delta t}{t} \times 100=1 \%
Heat produced, H=I2RtH=I^2 R t
Maximum possible error in heat produced,
=ΔHH×100=2(ΔII×100)+ΔRR×100+Δtt×100=2×2%+1%+1%=6%\begin{aligned} & =\frac{\Delta H}{H} \times 100 \\ & =2\left(\frac{\Delta I}{I} \times 100\right)+\frac{\Delta R}{R} \times 100+\frac{\Delta t}{t} \times 100 \\ & =2 \times 2 \%+1 \%+1 \%=6 \% \end{aligned}

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