# 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 : Option 1) series with C and has a magnitude   Option 2)  series with C and has a magnitude     Option 3)  parallel with C and has a magnitude Option 4) parallel with C and has a magnitude

V Vakul

As we learnt in

Power factor -

Ratio of resistance and impedance$(cos\phi)$.

-

$\therefore \frac{1}{\omega C} > \omega L -------- 1$

After inserting $c^{/}$ both become equal since $cos \phi = \frac{R}{Z} = 1$

or $R^{2} = R^{2} + {(X_{L} - X _{C})}^{2}$

$=> X_{L} = X _{C} -------- 2$

This implied $X_{c}$ must reduced

This will happen when C is increased.

$\therefore$ $C'$ must be inserted in parellel to $C$.

$\therefore \omega L = \frac{1}{\omega (C+C')}$

or $C+C' = \frac{1}{\omega ^{2}L}$ or $C^{/} = \frac{1}{W^{2}L} - C$

or $C' = \frac{1 - \omega ^{2} LC}{\omega ^{2}L}$

Option 1)

series with C and has a magnitude

This is incorrect option.

Option 2)

series with C and has a magnitude

This is incorrect option.

Option 3)

parallel with C and has a magnitude

This is incorrect option.

Option 4)

parallel with C and has a magnitude

This is correct option.

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