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Capacitance of a Random Conductor

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Question

Calculate the value of additional capacitor which may be joined suitably to the capacitor $C$ that would make the power factor of the circuit unity.

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Solution

Power factor is given by $c o s ϕ = 1$

⟹ $ϕ = 0^{o}$

⟹ $t a n ϕ = 0$

⟹ $X_{L} = X_{C} = 100 Ω$

⟹ $C = 10 μ F$

Hence a $8 μ F$ capacitor need to be connected in parallel with the given capacitor.

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