A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80 Ω, an inductor of inductive reactance X(L) = 70 Ω, and a capacitor of capacitive reactance X(C) = 130 Ω. The power factor of circuit is x/10. The value of x is :
Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit
JEE Mains 25 January 2023 Shift 2 Evening Shift

Question

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80 Ω, an inductor of inductive reactance X(L) = 70 Ω, and a capacitor of capacitive reactance X(C) = 130 Ω. The power factor of circuit is x/10. The value of x is :

Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit

JEE Mains 25 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Net reactance magnitude is |X(C) - X(L)| = 60 Ω. Therefore impedance Z = √(R² + X²) = √(80² + 60²) = 100 Ω. Power factor cosϕ = R/Z = 80/100 = 8/10. Hence x = 8.