College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
An RLC series circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) connected in series with an AC power source. This type of circuit can exhibit resonance, where the inductive and capacitive reactances cancel each other out.
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At resonance, the impedance of an RLC series circuit is purely resistive and equal to the resistance value $R$.
The resonant frequency $f_0$ is given by the formula $f_0 = \frac{1}{2\pi \sqrt{LC}}$.
The quality factor $Q$ is a measure of how underdamped the circuit is and can be calculated as $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$.
In an RLC series circuit, the total voltage across the components equals the supply voltage due to Kirchhoff's Voltage Law (KVL).
The phase angle between the total voltage and current depends on whether the circuit is inductive or capacitive; it is zero at resonance.
Review Questions
What happens to the impedance of an RLC series circuit at its resonant frequency?
How do you calculate the resonant frequency of an RLC series circuit?
Explain how to determine whether an RLC series circuit is predominantly inductive or capacitive.
Related terms
Impedance: The total opposition that a circuit offers to alternating current, represented as a complex number combining resistance and reactance.
Resonance: A condition in which inductive reactance equals capacitive reactance, resulting in maximum current flow in a series RLC circuit.
Quality Factor: $Q$ factor represents how underdamped a resonator is and relates to bandwidth; higher $Q$ indicates lower energy loss relative to stored energy.