After their values have been determined, Z can be found.įigure 3 Vectors for the current and the three different voltages in the RLC series circuit.īecause a capacitor and an inductor have opposite effects, their corresponding vectors are opposite to each other, and, thus, their sum is represented by a number smaller than the larger value ( X C – X L or X L – X C.įigure 4 illustrates two cases, one when X C > X L and one when X C X L, then the current leads the voltage and if X C < X L, the current lags the voltage. Z is the vector sum of these three values. This implies that R, X C, and X L cannot be algebraically added together. Nevertheless, remember that the scale for current and voltage can be different, whereas the scale for all identical values (voltages here) must be the same.Īs can be seen in Figure 3, the voltage across R is in phase with the current, the voltage across L is leading the current, and the voltage across C is lagging the current. Because the three components have the same current, the most appropriate reference entity for showing the vectors is the circuit current I.įigure 3 shows these vectors, irrespective of their numerical values (because we do not have any number of values given yet) but with the correct orientation. We now try to show these variables in the vector form. The voltage across the resistor is in phase with the current, the voltage across the capacitor is lagging the current by 90° and the voltage across the inductor leading the current by 90°. Recall that each of these voltages follows the rules that we learned about the relationship between current and voltage in each component. In this regard, the corresponding voltages across R, L, and C are denoted by V R, V L, and V C, respectively. The applied voltage in this circuit is divided between the three components. You May Also Read: Parallel RLC Circuit: Analysis & Example Problems.In the above circuit (Figure 1) V is the applied voltage, I is the common current for all the three elements, f is the frequency, and R, L, and C represent the values for resistance, inductance, and capacitance, respectively, of the three components in the circuit.
#Easy power electrical analysis examples series
The simplest question with a series RLC circuits is finding the current in the circuit if the particulars of the loads and the applied voltage are given. In tackling the circuit at hand, we need to know the relationship between the applied voltage and the current and the power consumption of the circuit, using all the knowledge that has been gained so far. Thus, in Figure 2 the two circuits are equivalent.įigure 2 Two equivalent Series RLC circuits. Note that the order the three components are shown is not important. Earlier it was shown that the impedance of a resistor is constant and real, in other words a resistor does not cause a phase shift between voltage and current as do capacitors and inductors.If any of the components is absent (usually, the inductor or the capacitor, not the resistor), then in calculations, the corresponding value for that element can be set to zero or the associated term deleted from the formulae.įigure 1 illustrates a series RLC circuit. It is important to note that the impedance of a capacitor or an inductor is a function of the frequency f and is an imaginary quantity - however is certainly a real physical phenomenon relating the shift in phases between the voltage and current phasors due to the existance of the capacitor or inductor. Let v(t) be a sinusoidal function of time with constant peak amplitude Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): Reactance Thus, all of the voltages and currents in the circuit are sinusoidal and have constant peak amplitude, frequency and phase. It can be shown that if the voltage and/or current sources in the circuit are sinusoidal and of constant frequency, the solutions tend to a form referred to as AC steady state. In general, the solutions for the voltages and currents in a circuit containing resistors, capacitors and inductors (in short, all linear behaving components) are solutions to a linear ordinary differential equation.
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