## Series R-L-C Circuit With Sinusoidal Applied Voltage

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By the principle of superposition, the transient and steady-state conditions are the same for the actual circuit and the equivalent circuit shown in Fig. 19, the closing of the switch occurring at time t = 0. In the equivalent circuit, the steady state is due to the source e acting continuously from time t = —, while the transient is due to short-circuiting the source —e at time t=0

The transient is found by determining current i = I and capacitor voltage e = E0 at time t = 0, due to the source — e. These values of I and E0 are then substitute d in the equations of Case 1, 2, 3, or 4, above, according to the values of R, L, and C.

This form of analysis may be used for any periodic applied voltage e. The steady-state current and the capacitor voltage for an applied voltage —e are determ ined, the periodic voltage being resolved into its harmonic components for this purpose, if necessary. Then the instantaneous values i I and e = E0 at the time of closing the switch are easily found, from which the transient is determined. It is evident, from this method of analysis, that the waveform of the transient need bear no relationship to that of the applied voltage, depending only on the constants of the circuit and the hypothetical initial conditions I and E0.

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The 2005 Ford Escape Hybrid is basically an electric car with a gasoline engine back up. This car is powered by Ford Duratec 2.3L 4-cylinder gasoline engine matched up with a 70KW (equivalent to 94hp) permanent magnet traction motor. The electric motor can propel the car on its own or in concert with gasoline engine to provide performance equivalent to a conventional V-6.

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The DIAC, or diode for alternating current, is a trigger diode that conducts current only after its breakdown voltage has been exceeded momentarily. Most DIAC have a breakdown voltage around 30 V. The DIAC is widely used in both industrial applications, such as hand tools and in lighting applications, specifically electronic lamp ballasts, the electric transformer for halogen lamps and light dimmers. (click image to enlarge).

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