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NEET
Exam
NEET
Subject
Physics
Chapter
Mathematics in Physics

NEET · Physics · Mathematics in Physics

The heat dissipated in a resistor is given by the formula H = I^2 R...

The heat dissipated in a resistor is given by the formula H=I2RtH = I^2 R t. In a laboratory experiment, the measured values of current (II), resistance (RR), and time (tt) are recorded as I=(10±0.2) AI = (10 \pm 0.2)\text{ A}, R=(5±0.1) ΩR = (5 \pm 0.1)\ \Omega, and t=(100±1) st = (100 \pm 1)\text{ s}. The maximum percentage error in the calculated value of heat dissipated HH will be:

Options

  1. A5%5\%
  2. B1.3%1.3\%
  3. C7%7\%
  4. D3%3\%

Correct answer

C. 7%7\%

Step-by-step solution

Percentage error in current I=0.210×100=2%I = \dfrac{0.2}{10} \times 100 = 2\%

Percentage error in resistance R=0.15×100=2%R = \dfrac{0.1}{5} \times 100 = 2\%

Percentage error in time t=1100×100=1%t = \dfrac{1}{100} \times 100 = 1\%

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

The maximum percentage error in HH is given by:
ΔHH×100=2(ΔII×100)+ΔRR×100+Δtt×100\dfrac{\Delta H}{H} \times 100 = 2\left(\dfrac{\Delta I}{I} \times 100\right) + \dfrac{\Delta R}{R} \times 100 + \dfrac{\Delta t}{t} \times 100

ΔHH×100=2(2%)+2%+1%=4%+2%+1%=7%\dfrac{\Delta H}{H} \times 100 = 2(2\%) + 2\% + 1\% = 4\% + 2\% + 1\% = 7\%

Answer: 7%7\%
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