A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is

Question

A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is (A) 0.33 (B) 0.56 (C) 0.64 (D) 0.80

Tardigrade Admin · Accepted Answer

XL=31 Ω, XC=25 Ω, R=8 Ω Impedance of series L C R is mathrmZ=√( mathrmR2)+( mathrmX mathrmL- mathrmX mathrmC)2 =√(8)2+(31-25)2=√64+36=10 Ω Power factor, cos φ=(R/Z)=(8/10)=0.8

Q. A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is

0.33

0.56

0.64

0.80

$X_{L} = 31Ω, X_{C} = 25Ω, R = 8Ω$
Impedance of series $L CR$ is
$Z = (R^{2}) + (X_{L} - X_{C})^{2}$
$= (8)^{2} + (31 - 25)^{2} = 64 + 36 = 10Ω$
Power factor, $cos ϕ = \frac{R}{Z} = \frac{8}{10} = 0.8$

Q. A coil of inductive reactance 31 Ω has a resistance of 8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω. The combination is connected to an ac source of 110 V . The power factor of the circuit is

0.33

0.56

0.64

0.80

XL​=31Ω,XC​=25Ω,R=8Ω Impedance of series LCR is Z=(R2)+(XL​−XC​)2​ =(8)2+(31−25)2​=64+36​=10Ω Power factor, cosϕ=ZR​=108​=0.8

$X_{L} = 31Ω, X_{C} = 25Ω, R = 8Ω$
Impedance of series $L CR$ is
$Z = (R^{2}) + (X_{L} - X_{C})^{2}$
$= (8)^{2} + (31 - 25)^{2} = 64 + 36 = 10Ω$
Power factor, $cos ϕ = \frac{R}{Z} = \frac{8}{10} = 0.8$