To reduce the reasonant frequency in an LCR series circuit with a generator

EXPLANATION:

→The frequency at which the impedance becomes minimum or current becomes maximum of the LCR circuit is called the Resonant frequency.

→The resonant frequency is also called the natural frequency of the LCR circuit.

→At resonance, the reactance of the inductor and capacitor becomes equal.

∴ X_L = X_C

⇒ \(\omega_0 L =\frac{1}{\omega_0 C} \)

⇒ ω0 = \(\frac{1}{\sqrt{LC}} \) rad/sec    ---- (1)

⇒f₀ = \(\frac{1}{2π\sqrt{LC}} \) Hz    ---- (2)

Where, ω0 = resonant frequency (angular), f0 = resonant frequency (linear) = ω0/2π

→From (2) we can say the following,

If L and C increase the resonant frequency will reduce.

If we add another capacitor parallel to C, the equivalent capacitance will increase.

And hence, the resonant frequency will decrease.

So, the correct answer is option (2).