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

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

Why the Circuit Power factor  (Cos θ) Decreases, when Inductance (L) or inductive reactance (XL) increases, In inductive circuit?
OR
Explain the statement that  “ the Circuit Power factor  (Cos θ) Decreases, when Inductance (L) or inductive reactance (XL) increases”

Explanation:
Suppose,
when Inductance (L) = 0.02H

V=220, R= 10 Ω, L=0.02 H, f=50Hz.

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

Z = √ (R2+XL2) = √ (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.
XL = 2πfL= 2 x 3.1415 x 50 x 0.04 = 12.56 Ω
Z = √ (R2+XL2) = √ (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 XL increases, the circuit power factor also Decreases.

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