Series Resistor-Inductor-Capacitor Circuit

Phaser diagram of voltage through inductance (VL), capacitance (VC), and resistance (VK) for alternating current circuit. Source Halliday, D., R. Resnick, and J. Walker. 2008. Fundamentals of Physics, 8th ed. New York John Wiley Sons, pp. 600-900. With permission.) 

Electric circuit schematic of resistor, inductor, and capacitor (RLC) connected in series. 

According to the circuit loop rule, the sum of the potentials through each element must be equivalent to the driving potential applied  

By rearranging Equation (1.64), a function for the current is then obtained  

The current is equal to the driving potential divided by a denominator term, hereafter known as impedance of an AC RLC circuit  

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From the expression in Eq. (19) most forms of equivalent circuit models of piezoelectric elements may be found. The Van Dyke circuit [14] is the simplest, using discrete electrical components combined to approximate the piezoelectric element s behavior. I tis used to represent the electrical irrqtedance about one resonance of a freely suspended piezoelectric element, using a shunt capacitor in parallel with an inductor, resistor, and capacitor placed in series to represent the motional or resonance behavior of the element. A multivibrator Van Dyke model may be formed by adding additional motional legs, each representing another resonance. Since it lacks any explicit treatment of the output force and velocity, it is not especially useful beyond electrical characterization (see... 

A resonator is characterized by a transfer function showing a narrow frequency bandwidth. In its simplest expression, it can be represented by a circuit consisting of three elements in series, an inductor L, a capacitor C and a resistor R, the latter reflecting the damping of the system. The important parameters are the resonance frequency fo in the absence of damping and the quality factor Q ... 

In the parallel configuration, the same potential difference occurs across each and every element with the total current being the algebraic sum of the current flowing through each individual circuit element. Table 2-35 summarizes the equivalent resistance, conductance, capacitance, and inductance of series-parallel configurations of resistors, capacitors, and inductors. 

The simple series RLC electrical circuit of Fig. 9.2 consists of a direct-current (DC) power source (here a 3-V battery), a relay, and three loads in series a resistor of resistance R, a capacitor of capacitance C, and an inductor of inductance L. Assume first a DC potential E = E0, in series with R, C, and L the capacitance stores charge, the inductance stores current, and the resistance dissipates some of the current into Joule13 heating. The arrow shows the direction of the current (which, thanks to Franklin s unfortunate assignment, is the direction of motion of positive holes—that is, the opposite of the flow of negative electrons) the relay across L avoids conceptual difficulties about an initial current through the inductor. The current is usually denoted by I (from the French word "intensite"). These three components (R, C, and L) will be explored in sequence. 

Equivalent circuit models have been used to represent piezoelectric material behavior for many years, but are not without limitations. The most common representation for a piezoelectric material, as recommended by the IRE/IEEE standards on piezoelectricity, is the Van Dyke model as described in detail in piezoelectric materials in microfluidics, with a capacitor, resistor, and inductor in series representing a single resonance, or motional component of the piezoelectric element, all set in parallel with a second capacitor, representing the shunt capacitance. Additional resonances may be included by placing additional... 

The Z-source DC circuit breaker basically consists of a silicon controlled rectifier (SCR) and two crossed L-C series connections. In case there is no fault, the SCR is on and the capacitors are charged by the voltage source. In steady state, the capacitor currents are zero, the voltages across the inductor vanish and a constant current fiows through the series connection of inductors and load. Suppose that the resistances of the inductors can be neglected and that the load is the parallel connection of a load resistor Rl and a load capacitor Cl - Then steady-state values are ... 

The total impedance of a system is the sum of the impedance of the electrical elements in the circuit such as resistors, capacitors, and inductors. For linear impedance elements in series, the equivalent impedance can be calculated from ... 

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