GATE EE 2017 Set 1 — Question 23
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Electrical & Electronic Measurements → Electrical Quantity Measurement → Error Analysis
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Question
The following measurements are obtained on a single phase load: , and . If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ______. (Give answer up to one decimal place.)
Correct answer
4 to 4.1
Solution
The power factor () is calculated as:Taking the natural logarithm on both sides:Differentiating to find the relative error:For the worst-case error, we sum the absolute values of the individual relative errors:Given:Thus, the worst case error in the calculated power factor is .
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