What effect does increasing the capacitance have in a resonant circuit?

What effect does increasing the capacitance have in a resonant circuit?

• A. Increases the resonant frequency
• B. Decreases the resonant frequency
• C. Does not affect the resonant frequency
• D. Increases the overall impedance

Answer: (B)

Increasing the capacitance in a resonant circuit decreases the resonant frequency. This relationship is governed by the formula for the resonant frequency of a circuit, which is expressed as: \[ f_r = \frac{1}{2\pi\sqrt{LC}} \] where \( f_r \) is the resonant frequency, \( L \) is the inductance, and \( C \) is the capacitance. According to this formula, as the capacitance \( C \) increases, the denominator in the equation (specifically, the term \( \sqrt{LC} \)) also increases, leading to a decrease in the overall value of the resonant frequency \( f_r \). Therefore, for a resonant circuit, increasing the capacitance effectively lowers the resonant frequency, allowing the circuit to resonate at a lower frequency. This principle is fundamental to understanding how resonant circuits operate, particularly in applications involving filters and oscillators.

Increasing the capacitance in a resonant circuit decreases the resonant frequency. This relationship is governed by the formula for the resonant frequency of a circuit, which is expressed as:

[ f_r = \frac{1}{2\pi\sqrt{LC}} ]

where ( f_r ) is the resonant frequency, ( L ) is the inductance, and ( C ) is the capacitance. According to this formula, as the capacitance ( C ) increases, the denominator in the equation (specifically, the term ( \sqrt{LC} )) also increases, leading to a decrease in the overall value of the resonant frequency ( f_r ).

Therefore, for a resonant circuit, increasing the capacitance effectively lowers the resonant frequency, allowing the circuit to resonate at a lower frequency. This principle is fundamental to understanding how resonant circuits operate, particularly in applications involving filters and oscillators.