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QJEEM22Ph59b7: JEE Main 2022 Physics - Class 11 JEEM22Ph59b7 Solution: The maximum error in the measurement of resistance, current and …

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%,2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be :

Multiple Choice Options

  • A 2
  • B 4
  • C 6
  • D 8

Step-by-Step Verified Solution

Given, ΔRR×100=1%\frac{\Delta R}{R} \times 100=1 \%

ΔFF×100=2% and Δtt×100=3%

We know that, heat produced due to current flowing through a resistor RR .

H=I2RtH =I^{2} R t

⇒ΔHH=2ΔII+ΔRR+Δtt\Rightarrow \frac{\Delta H}{H} =\frac{2 \Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}

⇒ΔHH×100=2(ΔII×100)+ΔRR×100+Δtt×100\Rightarrow \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

=2×2%+1%+3%=8%=2 \times 2 \%+1 \%+3 \%=8 \%

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