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 : (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

cos φ=(R/Z)=( R /√ R 2+( X C - X L )2) cos φ=(80/√(80)2+(60)2) cos φ=(80/100) ⇒ (8/10) So, x=8

Q. A series LCR circuit is connected to an AC source of 220V,50Hz. The circuit contains a resistance R=80Ω, an inductor of inductive reactance XL​=70Ω, and a capacitor of capacitive reactance XC​=130Ω. The power factor of circuit is 10x​. The value of x is :

cosϕ=ZR​=R2+(XC​−XL​)2​R​ cosϕ=(80)2+(60)2​80​ cosϕ=10080​⇒108​ So, x=8

$cos ϕ = \frac{R}{Z} = \frac{R}{R ^{2} + ( X _{C} - X _{L} ) ^{2}}$
$cos ϕ = \frac{80}{( 80 ) ^{2} + ( 60 ) ^{2}}$
$cos ϕ = \frac{80}{100} \Rightarrow \frac{8}{10}$
So, $x = 8$