Module-4 Single phase AC circuits

There are six lessons (4.1-4.6) in this module, where the various aspects related to ac circuits fed from single phase supply, are described.

**4.1** **Generation of single phase ac and fundamental aspects**

The principle of generation of sinusoidal (ac) waveforms (single phase) in an ac generator is first presented. Then, the two aspects – average and root mean square (rms) values, of alternating or periodic waveforms, such as voltage/current, are described with typical examples (sinusoidal and triangular).

**4.2** **Representation of sinusoidal quantities in phasor with j operator**

As the phasor relations are widely used for the study of single phasor ac circuits, the phasor representation of sinusoidal quantities (voltage/current) is described, in the lesson, along with the transformation from rectangular (Cartesian) to polar form, and vice versa. Then, the phasor algebra relating the mathematical operations, involving two or more phasors (as the case may be), from addition to division, is taken up, with examples in each case, involving both the forms of phasor representations as stated.

**4.3** **Steady state analysis of series circuits**

The steady state analysis of series (R-L-C) circuits fed from single phase ac supply is presented. Staying with each of the elements (R, L & C), the current in steady state is obtained with application of single phase ac voltage, and the phasor diagrams are also drawn in each case. The use of phasor algebra is also taken up. Then, other cases of series circuits, like R-L, R-C and R-L-C, are described, wherein, in each case, all methods as given, are used.

**4.4** **Analysis of parallel and series-parallel circuits**

The application of phasor algebra to solve for the branch and total currents and the complex impedance, of the parallel and the series-parallel circuits fed from single phase ac supply is presented in this lesson. The phasor diagram is drawn showing all currents, and voltage drops. The application of two Kirchoff’s laws in the circuits, for the currents at a node, and the voltage drops across the elements, including voltage source(s), in a loop, is shown there (phasor diagram).

**4.5** **Resonance in electrical circuits**

The problem of resonance in the circuits fed from a variable frequency (ac) supply is discussed in this lesson. Firstly, the case of series (R-L-C) circuit is taken up, and the condition of resonance, along with maximum current and minimum impedance in the circuit, with the variation in supply frequency is determined. Then, the problem of parallel circuits and other cases, such as, lossy coil (r-L), is taken up, where the condition of resonance is found. This results in minimum current and maximum impedance here.

**4.6** **Concept of apparent, active and reactive power**

The formula for active (average) power in a circuit fed from single phase ac supply, in terms of input voltage and current, is derived in this lesson, followed by definition of the

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term, ‘power factor’ in this respect. The concept of apparent and reactive power (with its sign for lagging and leading load) is presented, along with formula.

Module-5 Three phase AC circuits

There are only three lessons (5.1-5.3) in this module. Only the balanced star-and delta-connected circuits fed from three-phase ac supply are presented here.

**5.1 Generation of three-phase voltage, line and phase quantities in star- and delta-connection and their relations**

The generation of three-phase balanced voltages is initially presented. The balanced windings as described can be connected in star- and delta-configuration. The relation between line and phase voltages for star-connected supply is presented. Also described is the relation between phase and line currents, when the windings are connected in delta. The phasor diagrams are drawn for all cases.

**5.2** **Solution of three-phase balanced circuits**

The load (balanced) is connected in star to a balanced three-phase ac supply. The currents in all three phases are determined, with phasor diagram drawn showing all voltages and currents. Then, the relation between phase and line currents is derived for balanced delta-connected load. The power (active) consumed in the balanced load is derived in terms of the line voltage and currents for both cases.

**5.3** **Measurement of three-phase power**

The total power (in all three phases) is measured using two wattmeters only. This is shown for both unbalanced and balanced cases. The phasor diagram with balanced three-phase load is drawn. Other cases are also described.

Module-6 Magnetic circuits & Core losses

In this module there are two Lessons 21 and 22 as enumerated below.

**6.1** **Simple magnetic circuits**

It is often necessary to produce a desired magnetic flux, in a magnetic material (core) having a definite geometric shape with or without air gap, with the help of current passing through a coil wrapped around the core. This lesson discusses how the concept of circuit analogy can be introduced to tackle such problems. Both linear and non-linear magnetic circuit problems are discussed through worked out problems.

**6.2** **Eddy current & hysteresis losses**

These two losses are produced in any magnetic material which is subjected to an alternating time varying fields. Generally in all types of A.C machines /equipments working on electromagnetic principle these losses occur. In D.C machine armature too these losses occur. In this lesson the origin of these losses are explained and formula for estimating them are derived. Finally methods adopted to minimize these losses discussed as losses bring down the efficiency of any machines.

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