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:

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:,

MARKS App · Accepted Answer

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 .

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