# Power Factor of RC Circuit

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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
A. 1/√2
B. 2/√2
C.1/√5
D.1/2√2
Select the correct answer from the above-given options.

## 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+XC2)=1/√2

√2R=√(R2+XC2)

2R2-R2=XC2

⇒R=XC

When the frequency is halved

XC=1/2πfC=1/2π(f/2)C=2/2πfC

XC is doubled

⇒XC=2XC=2R

Now the power factor

cos ∅ =R/Z=R/√(R2+XC‘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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