f V = (100 ± 3)V and I = (10 ± 0.2)A. Find the percentage error in R? (R = V / I) 

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  1. 3.2%
  2. 3%
  3. 5%
  4. 10.2%

Answer (Detailed Solution Below)

Option 3 : 5%
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The correct answer is 5%.

Key Points

  • The formula for resistance (R) is given by R = V / I, where V is voltage and I is current.
  • For percentage error in R, the formula is: % error in R = % error in V + % error in I.
  • Percentage error in V = (3 / 100) × 100 = 3%, and percentage error in I = (0.2 / 10) × 100 = 2%.
  • Total percentage error in R = 3% + 2% = 5%, or 0.05 in decimal form.
  • Thus, the correct answer is Option 3: 0.05.

Additional Information

  • Percentage Error:
    • It represents the relative error in a measurement expressed as a percentage.
    • Calculated using the formula: (Error / Measured Value) × 100.
  • Significant Figures:
    • Significant figures are digits in a measurement that contribute to its accuracy.
    • They include all certain digits plus one estimated digit in a measurement.
  • Ohm's Law:
    • It states that the current through a conductor between two points is directly proportional to the voltage across the two points.
    • Expressed as V = IR, where V is voltage, I is current, and R is resistance.
  • Sources of Error in Measurements:
    • Instrumental Errors: Caused by imperfections in measuring devices.
    • Environmental Errors: Arise from external factors like temperature, humidity, etc.
    • Human Errors: Caused by the observer's mistakes during measurement.
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