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:

Step-by-step solution

Power factor in LCR circuit is given by, cos   ϕ = R Z , where, Z is the total impedance of the circuit. So, cos ϕ = R R 2 + X C - X L 2 Putting the values, we have ⇒ cos   ϕ = 80 ( 80 ) 2 + ( 60 ) 2 ⇒ cos   ϕ = 80 100 ⇒ 8 10 Thus, the value of x = 8 .