Q45. A series LCR circuit is driven by an rms voltage of 90 V at frequency 30 Hz. At this frequency the circuit has resistance R = 80 Ω, inductive reactance $X_{L}$ = 20 Ω and capacitive reactance $X_{C}$ = 80 Ω. What is the power factor of the circuit?
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Question

Q45. A series LCR circuit is driven by an rms voltage of 90 V at frequency 30 Hz. At this frequency the circuit has resistance R = 80 Ω, inductive reactance $X_{L}$ = 20 Ω and capacitive reactance $X_{C}$ = 80 Ω. What is the power factor of the circuit?

Options

G1 Physics · Accepted Answer

For a series LCR circuit, Z = √[R² + (X(L)-X(C))²]. Substitute: Z = √[80² + (20-80)²] = √(6400+3600) = √10000 = 100 Ω. The power factor is cosφ = R ÷ Z = 80 ÷ 100 = 0.80. Correct option: A.

Q45. A series LCR circuit is driven by an rms voltage of 90 V at frequency 30 Hz. At this frequency the circuit has resistance R = 80 Ω, inductive reactance X L X_{L} X L ​ = 20 Ω and capacitive reactance X C X_{C} X C ​ = 80 Ω. What is the power factor of the circuit?

Q45. A series LCR circuit is driven by an rms voltage of 90 V at frequency 30 Hz. At this frequency the circuit has resistance R = 80 Ω, inductive reactance X L X_{L} X L = 20 Ω and capacitive reactance X C X_{C} X C = 80 Ω. What is the power factor of the circuit?