Free Oscillations in RLC Circuits

 The processes that take place in a circuit after it has been forced out of equilibrium and is set free afterwards are called free processes. In a circuit with a capacitor (C) , an inductor (L) and a resistor (R) , these processes will assume a character of oscillations. An initial disturbance can be a charge on the capacitor Q0 that occurs before the connection is made. In an ideal circuit without resistance-based losses (R = 0) , free non-damped oscillations occur at the natural frequency of the circuit: ω0 = 2π/T. This process can last an infinitely long time. Twice in a given period, the energy that is stored in the capacitor transfers to the magnetic energy of the inductor. With the energy losses (R ≠ 0) , damped oscillations occur in the circuit. The amplitude of the oscillations decreases exponentially over time. The time required for the amplitude to decrease by a factor of e=2.7 is called the relaxation time. It equals 2L/R. As the resistance R increases, the relaxation time approaches the period T. In such a case, the free process in the circuit ceases to be an oscillating one. In real circuits, energy losses are always present. Eventually, all of the electric energy that was initially stored in the capacitor becomes heat, and is released to the resistor.