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JEE Main 201219 MayOnline
Exam
JEE Main
Year
2012
Date
19 May
Mode
Online
Subject
Physics
Chapter
Mathematics in Physics

JEE Main 2012 · 19 May · Online · Physics · Mathematics in Physics

The amount of heat produced in an electric circuit depends upon the...

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

Options

  1. A1%1 \%
  2. B2%2 \%
  3. C6%6 \%
  4. D3%3 \%

Correct answer

C. 6%6 \%

Step-by-step solution

Given : ΔII×100=2%\frac{\Delta I}{I} \times 100=2 \%; ΔRR×100=1%and\frac{\Delta R}{R} \times 100=1 \% and\frac{\Delta t}{t} \times 100=1 \%Heatproduced,Heat produced,H=I^2 R tMaximumpossibleerrorinheatproduced,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} \times100 \\ & =2\left(\frac{\Delta I}{I} \times100\right)+\frac{\Delta R}{R} \times₁₀₀⁺\frac{\Delta t}{t} \times100 \\ & =2 \times2 \%+1 \%+1 \%=6 \% \end{aligned}$
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