The power factor of an R-L circuit is 1/√(2). If the frequency of AC is doubled the power factor will now be (a) 1/√(3) (b) 1/√(5) (c) 1/√(7) (d) (1)/(√(11))

Answer: (b). cos φ = (R)/(√(R² + XL²)) = 1/√(2) ⇒ XL = R. XL = 2π fL, so doubling f gives XL' = 2R. cos φ' = (R)/(√(R² + 4R²)) = 1/√(5). So the answer is (b) 1/√(5).

The power factor of an R-L circuit is 1/√(2). If the frequency of AC… | MHT CET 2023 (14 May, Shift 2)

Q48MHT CET 2023 · 14 MAY · SHIFT 2Medium

Power, Power Factor & Wattless Current

The power factor of an R-L circuit is $\frac{1}{\sqrt{2}}$ . If the frequency of $AC$ is doubled the power factor will now be

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Answer: (b)

$\cos\phi = \frac{R}{\sqrt{R^2 + X_L^2}} = \frac{1}{\sqrt{2}} \Rightarrow X_L = R$ .
$X_L = 2\pi fL$ , so doubling $f$ gives $X_L' = 2R$ .
$\cos\phi' = \frac{R}{\sqrt{R^2 + 4R^2}} = \frac{1}{\sqrt{5}}$ .
So the answer is (b) $\frac{1}{\sqrt{5}}$ .

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Power, Power Factor & Wattless Current question from MHT CET 2023 (14 May, Shift 2)

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