Category: Single-phase AC Circuits

Consider a phasor  lying along OX-axis as shown in Figure 7.61. The phasor is reversed when it is multiplied by −1, that is, the phasor is rotated through 180° in counter clockwise (CCW) direction and attains the position along OX′-axis. Let us consider j as a factor which when multiplied by the phasor , the phasor is rotated through 90°…

Before applying the method of phasor algebra for solving parallel AC circuits, let us have an idea of important topics of phasor algebra. A technique, developed by engineers, to represent a phasor in an algebraic (i.e., mathematical) form is known as phasor algebra or complex algebra. This technique has provided a relatively simple but powerful…

Before applying this method for the solution of parallel AC circuits, the reader should be familiar with the following important terms: 7.19.1  Admittance The reciprocal of impedance of an AC circuit is called admittance of the circuit. Since impedance is the total opposition to the flow of AC in an AC circuit, the admittance is the…

To solve parallel AC circuits by this method, we proceed as follows: Step I: Draw the circuit as per the given problem, as shown in Figure 7.47(a) (here, for illustration, we have considered two branches connected in parallel. One branch contains resistance and inductance in series, whereas second branch contains resistance and capacitance in series. The supply voltage…

In parallel circuits, a number of branches are connected in parallel. Each branch, generally, contains number of components such as resistance, inductance, and capacitance forming series circuits. Therefore, each branch is analysed separately as a series circuit, and then, the effects of separate branches are combined together. While carrying out circuit calculations, the magnitudes and…

The AC circuits in which number of branches are connected in such a manner so that voltage across each branch is the same, but current flowing through them is different are called AC parallel circuits. The parallel circuits are used more frequently in AC system because of the following reasons:

The curve obtained by plotting a graph between the current and the frequency is known as resonance curve. A resonance curve of a typical R–L–C series circuit is shown in Figure 7.33. It may be noted that current reaches its maximum value at the resonant frequency (fr), falling off rapidly on either side of that point. It…

In an R–L–C series circuit, when circuit current is in phase with the applied voltage, the circuit is said to be in series resonance. This condition is obtained in an R–L–C circuit shown in Figure 7.31, Fig. 7.31  R–L–C series circuit when   XL = XC (or XL − XC = 0) At resonance,    XL − XC = 0 or XL = XC Impedance,  Current, Since at resonance, the opposition to…

A circuit that contains a pure resistance of R Ω, a pure inductance of L Henry, and a pure capacitor of capacitance C Farad; all connected in series is known as R–L–C series circuit. An R–L–C series circuit is shown in Figure 7.28. Fig. 7.28  Circuit containing resistance, inductance and capacitance in series Here, XL = 2 π ɸ L and XC = 1/2 π f C When a resulting current I (rms value) flows…