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Resonant frequency is a crucial concept in the study of RLC circuits, representing the frequency at which the circuit naturally oscillates with the least impedance. This particular frequency is dependent on both the inductance (L) and capacitance (C) of the circuit. It is given by the equation: \[ \text{Resonant Frequency} (f_0) = \frac{1}{2\pi\sqrt{LC}} \]. This expression indicates that the resonant frequency is inversely proportional to the square root of both the inductance and the capacitance.

When the circuit reaches its resonant frequency, its impedance is minimized, and the circuit can efficiently transfer energy between the inductor and capacitor. This property is widely used in various applications such as radio receivers and transmission antennas.

Inductance is a fundamental property of circuits, it describes the ability of an inductor to store energy in a magnetic field when electrical current flows through it. Measured in henrys (H), inductance is crucial in determining the behavior of alternating current (AC) circuits.

It is an inherent property of coils, represented mathematically by the letter L. In an RLC circuit, the inductance affects how the circuit reacts to changes in current. Particularly, in the context of resonant frequency, higher inductance will reduce the resonant frequency, as seen from the formula \( f_0 = \frac{1}{2\pi\sqrt{LC}} \).

Thus, when inductance values change, we can expect a corresponding impact on the resonant frequency of the circuit. Inductors are key components in tuning frequencies for filtering and oscillation in myriad electronics.

Capacitance is the ability of a component or circuit to store an electrical charge, and it plays a crucial role in tuning the frequency of an RLC circuit. Measured in farads ( F ), capacitance defines how much charge a capacitor can store per unit voltage.

Capacitance directly influences the resonant frequency alongside inductance. According to the formula for resonant frequency, increasing the capacitance of an RLC circuit decreases its resonant frequency. This makes capacitors indispensable for controlling signal frequencies within electronic devices.

In practical terms, capacitors are the components that hold energy within an RLC circuit, oscillating charge at a specific frequency that defines the resonant frequency the circuit will naturally settle on.

Frequency calculation in RLC circuits involves understanding the relationship between frequency and the circuit components: inductance and capacitance. The resonant frequency formula \( f_0 = \frac{1}{2\pi\sqrt{LC}} \) provides the foundation for these calculations.

When tasked with determining a new resonant frequency after modifying inductance, it's essential to maintain the capacitance constant. We use the known resonant frequency and parameters to first solve for the unknown capacitance. From there, employing the formula again allows recalculating the resonant frequency for changed inductance.

Specifically, to exemplify this calculation, if one reduces the inductance from 7.0 \( ext{mH}\) to 1.5 \( ext{mH}\) and knows the initial frequency, we can determine that: \[ f_2 = f_1 \times \sqrt{\frac{L_1}{L_2}} \]

This approach illustrates the inverse square root relationship between inductance and frequency, ensuring precise adjustments in real-world applications.