Question:
In an ac main, the rms voltage \( V_{ac} \), rms current \( I_{ac} \) and power \( W_{ac} \) are measured as:
\( V_{ac} = 100 \, \text{V} \pm 1% \), \( I_{ac} = 1 \, \text{A} \pm 1% \), \( W_{ac} = 50 \, \text{W} \pm 2% \)
The percentage error in calculating the power factor using these readings is
In an ac main, the rms voltage \( V_{ac} \), rms current \( I_{ac} \) and power \( W_{ac} \) are measured as:
\( V_{ac} = 100 \, \text{V} \pm 1% \), \( I_{ac} = 1 \, \text{A} \pm 1% \), \( W_{ac} = 50 \, \text{W} \pm 2% \)
The percentage error in calculating the power factor using these readings is
\( V_{ac} = 100 \, \text{V} \pm 1% \), \( I_{ac} = 1 \, \text{A} \pm 1% \), \( W_{ac} = 50 \, \text{W} \pm 2% \)
The percentage error in calculating the power factor using these readings is
Show Hint
When calculating percentage errors in a derived quantity like power factor, sum the percentage errors of the measured quantities involved.
Updated On: Jan 8, 2026
- 1%
- 2%
- 3%
- 4%
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The Correct Option is D
Solution and Explanation
We are given the values of rms voltage \( V_{ac} = 100 \, \text{V} \), rms current \( I_{ac} = 1 \, \text{A} \), and power \( W_{ac} = 50 \, \text{W} \), along with their respective percentage errors: 1% for voltage, 1% for current, and 2% for power. The power factor \( \cos \phi \) is defined as the ratio of real power \( W_{ac} \) to the product of rms voltage and rms current:
\[
\cos \phi = \frac{W_{ac}}{V_{ac} I_{ac}}.
\]
The percentage error in the power factor can be approximated by summing the percentage errors in the voltage, current, and power:
\[
\text{Percentage error in } \cos \phi \approx \text{Percentage error in } W_{ac} + \text{Percentage error in } V_{ac} + \text{Percentage error in } I_{ac}.
\]
Thus, the total percentage error is:
\[
2% + 1% + 1% = 4%.
\]
Final Answer: 4%
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