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Q. In a series LR circuit XL=R and power factor of the circuit is P1. When capacitor with capacitance C such that XL=XC is put in series, the power factor becomes P2. The ratio P1P2 is

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Solution:

In case of L-R circuit
Z=X2L+R2& power factor
P1=cosϕ=RZ
As XL=R
Z=2R
P1=R2RP1=12
In case of L-C-R circuit
Z=R2+(XLXC)2
As XL=XC
Z=R
P2=cosϕ=RR=1
P1P2=12