We create such open circuits everyday.įor example, to turn off a light, we need to break to flow of electrons. So, by definition, an /open circuit/is one where the continuity has been broken by an interruption in the path for electrons to flow. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the We indicate rms values with a subscript attached to a capital letter (such as I rms I rms).Īlthough a capacitor is basically an open circuit, an rms current, or the root mean square of the current, appears in a circuit with an ac voltage applied to a capacitor. Appliances and devices are commonly quoted with rms values for their operations, rather than peak values. As a result, the rms values of current and voltage are not zero. First, you square the function, next, you take the mean, and then, you find the square root. The rms operates in reverse of the terminology. Therefore, we often use a second convention called the root mean square value, or rms value, in discussions of current and voltage. However, if we average out the values of current or voltage, these values are zero. To this point, we have exclusively been using peak values of the current or voltage in our discussion, namely, I 0 I 0 and V 0. The current phasor leads the voltage phasor by π / 2 π / 2 rad as they both rotate with the same angular frequency. From Kirchhoff’s loop rule, the instantaneous voltage across the capacitor of Figure 15.7(a) isįigure 15.8 The phasor diagram for the capacitor of Figure 15.7. Now let’s consider a capacitor connected across an ac voltage source. The relative lengths of the two phasors are arbitrary because they represent different quantities however, the ratio of the lengths of the two phasors can be represented by the resistance, since one is a voltage phasor and the other is a current phasor. Since they have the same frequency and are in phase, their phasors point in the same direction and rotate together. For example, both the current i R ( t ) i R ( t ) and the voltage v R ( t ) v R ( t ) are shown in the diagram of Figure 15.6(b). In addition, several quantities can be depicted on the same phasor diagram. The vertical axis on a phasor diagram could be either the voltage or the current, depending on the phasor that is being examined. (b) The phasor diagram representing both i R ( t ) i R ( t ) and v R ( t ) v R ( t ). If the length of the arrow corresponds to the current amplitude I 0, I 0, the projection of the rotating arrow onto the vertical axis is i R ( t ) = I 0 sin ω t, i R ( t ) = I 0 sin ω t, which is the instantaneous current.įigure 15.6 (a) The phasor diagram representing the current through the resistor of Figure 15.5. The arrow (or phasor) is rotating counterclockwise at a constant angular frequency ω, ω, so we are viewing it at one instant in time. The phasor diagram for i R ( t ) i R ( t ) is shown in Figure 15.6(a), with the current on the vertical axis. Such representations are called phasor diagrams. Graphical representations of the phase relationships between current and voltage are often useful in the analysis of ac circuits. Both curves reach their maxima and minima at the same times, that is, the current through and the voltage across the resistor are in phase. Plots of i R ( t ) i R ( t ) and v R ( t ) v R ( t ) are shown in Figure 15.5(b). Here, I 0 = V 0 / R I 0 = V 0 / R is the amplitude of the time-varying current. (b) The current i R ( t ) i R ( t ) through the resistor and the voltage v R ( t ) v R ( t ) across the resistor. Figure 15.5 (a) A resistor connected across an ac voltage source.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |