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NEET
Exam
NEET
Subject
Physics
Chapter
Mathematics in Physics

NEET · Physics · Mathematics in Physics

The heat dissipated in a resistance wire is given by Joule's law of...

The heat dissipated in a resistance wire is given by Joule's law of heating, H=I2RtH = I^2 R t. In an experiment, the maximum percentage errors in the measurement of heat dissipated (HH), resistance (RR), and time (tt) are 9%9\%, 2%2\%, and 1%1\% respectively. The percentage error in the measurement of current (II) is:

Options

  1. A6%6\%
  2. B12%12\%
  3. C3%3\%
  4. D4.5%4.5\%

Correct answer

C. 3%3\%

Step-by-step solution

The formula for heat dissipated is H=I2RtH = I^2 R t.

The maximum percentage error in HH is given by the sum of the percentage errors of its factors, multiplied by their respective powers:
ΔHH×100=2(ΔII×100)+(ΔRR×100)+(Δtt×100)\dfrac{\Delta H}{H} \times 100 = 2 \left( \dfrac{\Delta I}{I} \times 100 \right) + \left( \dfrac{\Delta R}{R} \times 100 \right) + \left( \dfrac{\Delta t}{t} \times 100 \right)

Given the percentage errors:
ΔHH×100=9%\dfrac{\Delta H}{H} \times 100 = 9\%
ΔRR×100=2%\dfrac{\Delta R}{R} \times 100 = 2\%
Δtt×100=1%\dfrac{\Delta t}{t} \times 100 = 1\%

Substitute these values into the error equation:
9%=2(ΔII×100)+2%+1%9\% = 2 \left( \dfrac{\Delta I}{I} \times 100 \right) + 2\% + 1\%

9%=2(ΔII×100)+3%9\% = 2 \left( \dfrac{\Delta I}{I} \times 100 \right) + 3\%

2(ΔII×100)=9%−3%=6%2 \left( \dfrac{\Delta I}{I} \times 100 \right) = 9\% - 3\% = 6\%

ΔII×100=6%2=3%\dfrac{\Delta I}{I} \times 100 = \dfrac{6\%}{2} = 3\%

The percentage error in the measurement of current is 3%3\%.

Answer: 3%3\%
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