How does the resonant frequency change when the inductance is increased in an RLC circuit?

Specifically, when the inductance (L) in an RLC circuit is increased:

Lower Resonant Frequency: The resonant frequency of the RLC circuit decreases. This is because the resonant frequency (fr) is inversely proportional to the square root of the inductance, according to the formula:

fr = 1 / (2π√(LC))

When the inductance (L) increases, the denominator in the above formula increases, leading to a smaller resonant frequency.

Wider Bandwidth: The bandwidth of the RLC circuit also increases. Bandwidth is the range of frequencies around the resonant frequency where the circuit's response remains relatively low (close to the minimum). With higher inductance, the bandwidth broadens.

Slower Response: The transient response of the circuit to changes in the input voltage or current becomes slower with higher inductance.

Higher Impedance: At frequencies below the resonant frequency, the impedance of the circuit will be dominated by the inductive reactance (XL = 2πfL). Therefore, higher inductance will result in higher impedance at these frequencies.

Lower Impedance at Resonance: At the resonant frequency, the inductive reactance (XL) and capacitive reactance (XC = 1 / (2πfC)) will be equal and opposite in phase, leading to cancellation of the reactive components. This results in a lower overall impedance at resonance.

It's important to note that changes in the capacitance (C) or resistance (R) values of the RLC circuit will also affect the resonant frequency and other circuit characteristics. The resonant frequency is a valuable parameter in various applications, such as in filters, oscillators, and impedance matching circuits.