A series circuit has an impedance of $60.0 Ω$ and a power factor of $0.720$ at $50.0 H z$ . The source voltage lags the current. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor?

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Solution

Voltage lags
$∴ X_{C} > X_{L}$
Power factor, $cos ϕ = \frac{R}{Z}$
$= \frac{R}{\sqrt{R^{2} + (X_{C} - X_{L})^{2}}}$
To increase the power factor denominator should decrease. Hence $X_{L}$ should increase. Therefore an inductor is required to be connected.

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A series circuit has an impedance of 60.0Ω and a power factor of 0.720 at 50.0Hz. The source voltage lags the current. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor?

Voltage lags∴XC>XLPower factor, cosϕ=RZ=R√R2+(XC−XL)2To increase the power factor denominator should decrease. Hence XL should increase. Therefore an inductor is required to be connected.

A series circuit has an impedance of $60.0 Ω$ and a power factor of $0.720$ at $50.0 H z$ . The source voltage lags the current. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor?

Voltage lags
$∴ X_{C} > X_{L}$
Power factor, $cos ϕ = \frac{R}{Z}$
$= \frac{R}{\sqrt{R^{2} + (X_{C} - X_{L})^{2}}}$
To increase the power factor denominator should decrease. Hence $X_{L}$ should increase. Therefore an inductor is required to be connected.