Power Factor of RC Circuit

Answer: C.1/√5

The power factor of a series RC circuit is 1/√2. If the frequency of the applied AC is halved, the power factor will be 1/√5.

Solution:

Given that the power factor of the series RC circuit is 1/√2.

For series RC circuit power factor 

cos ∅ =R/Z=R/√(R²+X_C²)=1/√2

√2R=√(R²+X_C²)

2R²-R²=X_C²

⇒R=X_C

When the frequency is halved

X_C=1/2πfC=1/2π(f/2)C=2/2πfC

X_C is doubled

⇒X_C^‘=2X_C=2R

Now the power factor 

cos ∅ =R/Z=R/√(R²+X_C^‘2)=R/√(R²+(2R)²)=1/√5

Now power factor of the RC circuit is 1/√5.

Hence option C is the correct answer.

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