Why the Circuit Power factor (Cos θ) Decreases, when Inductance (L) or inductive reactance (XL) increases, In inductive circuit?

Explanation:  

Suppose, 

when Inductance (L) = 0.02H

V=220, R= 10 Ω, L=0.02 H, f=50Hz.

X_L = 2πfL = 2 x 3.1415 x 50 x 0.02 = 6.28 Ω

Z = √ (R²+X_L²) = √ (10² + 6.28²) = 11.8 Ω

Cos θ = R/Z = 10/11.05 = 0.85

 

Now we increases Inductance (L) form 0.02 H to 0.04 H,

V=220, R= 10 Ω, L=0.04 H, f=50Hz.

X_L = 2πfL= 2 x 3.1415 x 50 x 0.04 = 12.56 Ω

Z = √ (R²+X_L²) = √ (10² + 12.56²) = 16.05 Ω

Cos θ = R/Z = 10/16.05 = 0.75

 

Conclusion:

We can see that, When inductance (L) was 0.02, then circuit current were 18.64 A, and Circuit power factor was (Cos θ) = 0.85.

But, when Circuit inductance increased from 0.02H to 0.04 H, then  Power Factor (Cos θ) decreased from 0.85 to 0.75.

Hence proved,

In inductive circuit, when inductive reactance X_L increases, the circuit power factor also Decreases.