For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor $C^{'}$ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor $C^{'}$ , must have been connected in:

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Current is leading, it means inductive reactance is more than capacitive reactance For making power factor to be unity the value of C is to be increased.

$\Rightarrow$ another capacitor $C^{'}$ should be connected in parallel. So in that condition $X_{L} = X_{C}$

$\Rightarrow ω L = \frac{1}{ω C _{e q}} \Rightarrow C_{e q} = \frac{1}{ω ^{2} L}$

$\Rightarrow C + C^{'} = \frac{1}{ω ^{2} L} \Rightarrow C^{'} = \frac{1}{ω ^{2} L} - C$

$\Rightarrow C^{'} = \frac{1 - ω ^{2} L C}{ω ^{2} L}$

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