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Question
In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL= XC is put in series, the power factor becomes P2. The ratio `"P"_1/"P"_2` is ______.
Options
`1/2`
`1/sqrt2`
`sqrt3/sqrt2`
2:1
MCQ
Fill in the Blanks
Solution
In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL= XC is put in series, the power factor becomes P2. The ratio `"P"_1/"P"_2` is `underlinebb(1/sqrt2)`.
Explanation:
Given that power factor of the circuit is P1 when XL = R
P1 = `"R"/(sqrt("R"^2+("X"_"L"-"X"_"C")^2))=1/sqrt2` (∵ XC = 0)
Power factor of the circuit is P2, when XL = XC
P2 = `"R"/(sqrt("R"^2+("X"_"L"-"X"_"C"))^2)=1`
So, we have `"P"_1/"P"_2=1/sqrt2`
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