Alternating Current

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Forced Oscillations

We have seen that once started, the charge, potential difference, and current in both  undamped LC circuits and damped RLC circuits (with small enough R) oscillate at  angular frequency W  Such oscillations are said to be free oscillations (freeof any external emf), and the angular frequency W is said to be the circuit’s natural angular frequency.When the external alternating emf of  is connected to an RLC circuit, the oscillations of charge, potential difference, and current are said to be driven  oscillations or forced oscillations. These oscillations always occur at the driving angular frequency ~ Whatever the natural angular frequency t» of a circuit may be, forced oscillations of charge, current, and potential difference in the circuit always occur at the driving angular
frequency w”. Three Simple Circuits

Later in this chapter, we shall connect an external alternating emf device to a series RLC circuit as in Fig. 33-7. We shall then find expressions for the amplitude I and phase constant cp of the sinusoidally oscillating current in terms of the amplitude  ~m and angular frequency Wd of the external emf. First, however. let us considerthree simpler circuits, each having an external emf and only one other circuit element: R, C, or L. We start with a resistive element (a purely resistive load).

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