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10/01/2022 12:38 pm
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An ac circuit has an inductor and a resistor of resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is √5 : x. The value of x is _____.
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10/01/2022 12:51 pm
cos φ = \(\frac{R}{\sqrt{R^2 + 3R^2}}\) cos φ' = \(\frac{R}{\sqrt{R^2 + R^2}}\)
= \(\frac{1}{\sqrt{10}}\) = \(\frac{1}{\sqrt2}\)
\(\frac{cos \phi'}{cos \phi}\) = \(\frac{\sqrt{10}}{\sqrt 2}\)
= \(\frac{\sqrt5}{1}\)
∴ x = 1