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Alternating Current in the L-R-C Series Circuit 2
 
A pure LC circuit is useful as an idealized illustration of current oscillations, but any real inductor also has a resistance that eventually dissipates the energy. In series with a capacitor, it forms a circuit that exhibits both LC and LR circuit behavior: the current oscillates, but the oscillation damps exponentially.
When the resistance R is small, the circuit oscillates with nearly the natural frequency ω0=1/(LC)1/2.
When the applied frequency equals the natural frequency ω0, the current is in phase with the applied voltage, and the current amplitude is at maximum. You can observe this effect by calculating the natural frequency for your initial parameters (R and L) and make the applied frequency equal or nearly equal to the natural frequency using floating band control. After you have done this look at the graph. (If the graph is hidden you can make it visible using the checkbox). This phenomenon is known as a resonance.
A very useful tool which will help you to understand the process is a phase diagram. Check the checkbox labeled ?show phase? to see it. On the phase diagram each arrow symbolizes the potential difference on the corresponding part of the circuit, except one horizontal arrow which denotes the current. By comparing the arrow?s lengths you can compare the maximum values of the potential differences. The relative angles of the arrows correspond to the phase relationships between the potential differences. Change values of R, L and C and see how it is visualized by phase diagram.
 
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