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An RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. These components can store and release energy, creating oscillations in the circuit.
An underdamped RLC circuit is one in which the oscillations continue for a longer period of time without being fully damped or dissipated. This can occur when the resistance in the circuit is relatively low, causing the circuit to have a high quality factor (Q).
The time constant (τ) for an underdamped RLC circuit can be calculated using the formula τ = L/R, where L is the inductance of the circuit and R is the resistance. This value represents the time it takes for the circuit to reach 1/e (approximately 37%) of its initial charge or current.
The amount of damping in an RLC circuit is affected by the resistance, inductance, and capacitance of the circuit. Higher values of resistance and inductance will result in a more damped circuit, while a lower capacitance can also contribute to increased damping.
The damping ratio (ζ) for an underdamped RLC circuit can be calculated using the formula ζ = R/2√(L/C), where R is the resistance, L is the inductance, and C is the capacitance. This value represents the ratio of actual damping to critical damping, with a value less than 1 indicating underdamping.
