A LCR series circuit driven with at frequency has resistance , an inductance with inductive reactance and capacitance

Question

A LCR series circuit driven with $E_{rms} = 90 V$ at frequency $f_{d} = 30 Hz$ has resistance $R = 80 Ω$ , an inductance with inductive reactance $X_{L} = 20.0 Ω$ and capacitance with capacitive reactance $X_{C} = 80.0 Ω$ . The power factor of the circuit is ______. [2026]

Smart Achievers · Accepted Answer

(1)

$Power factor is \cos ϕ = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = 100 Ω$

$\cos ϕ = \frac{80}{100} = 0.8$

Solution

Q.
A LCR series circuit driven with $E_{rms} = 90 V$ at frequency $f_{d} = 30 Hz$ has resistance $R = 80 Ω$ , an inductance with inductive reactance $X_{L} = 20.0 Ω$ and capacitance with capacitive reactance $X_{C} = 80.0 Ω$ . The power factor of the circuit is ______. [2026]

1 0.8

2 0.64

3 0.9

4 0.5

Ans.
(1)

$Power factor is \cos ϕ = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = 100 Ω$

$\cos ϕ = \frac{80}{100} = 0.8$

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