The ideal resistor was a useful approximation of many practical electrical devices. However, in addition to resistance, which always dissipates energy, an electric circuit may also exhibit capacitance and inductance, which act to store and release energy, in the same way that an expansion tank and flywheel, respectively, act in …

Read More »## Phase Sequence in Three-Phase System

In a three-phase service supplied by an electrical utility company, all three line voltages have the same magnitude and are displaced from one another by 120°. We can measure the magnitude of these voltages quite readily. However, the magnitudes do not tell us whether VBN leads VAN by 120° or …

Read More »## Advantages of Polyphase System

The two-phase alternator in Figure 1(a) has two identical loops mounted on the same rotor. Since both loops have the same number of turns and rotate at the same angular velocity, the voltages induced in them have the same magnitude and frequency. Loop A is mounted on the rotor 90° …

Read More »## Hybrid Parameters of Two Port Network

For analyzing circuits containing active devices such as transistors, it is more convenient to think of the input terminals of a four-terminal coupling network as a Thévenin-equivalent voltage source and the output terminals as a Norton-equivalent current source. We then describe the coupling network in terms of four hybrid parameters …

Read More »## Short-Circuit Admittance Parameters

We can represent the generalized coupling network by the π-network shown with dotted lines in Figure 1. It is simpler to work with admittances when we encounter a coupling network in the form of a π-network, which is a dual for a T-network. Although the resulting short-circuit admittance parameters (y-parameters) …

Read More »## Open-Circuit Impedance Parameters

To define the composition of a four-terminal, two-port network, we need four parameters. The test circuit of Figure 1 gives a set of parameters called the open-circuit impedance parameters (z-parameters) of the network. Figure 1 Determining open-circuit impedance parameters We start by opening the right-hand switch in Figure 1 so …

Read More »## Impedance in Series and Parallel

Resistance and impedance both represent opposition to electric current. However, resistance opposes both direct and alternating current, while the reactance component of impedance opposes only changing current. Calculations for DC circuits can be done with scalar quantities and ordinary algebra. But impedance is a phasor quantity in AC circuits, and …

Read More »## Power Triangle and Power Factor in AC Circuits

Power Triangle The real power in the circuit of Figure 1 can be found from the product of VR and I, and the reactive power from the product of VL and I. Since VL leads VR by 90°, \[\begin{matrix}{{V}_{T}}=\sqrt{V_{R}^{2}+V_{L}^{2}} & {} & \left( 1 \right) \\\end{matrix}\] Figure 1 AC circuit …

Read More »## Parallel Circuit Characteristics

Resistance, Inductance, and Capacitance in Parallel Circuit The characteristic of a parallel circuit is that the same voltage appears across all parallel branches. We use this common voltage as the reference phasor in phasor diagrams for any parallel AC circuits. Ohm’s law then gives the current through each branch of …

Read More »## Phasor Diagram and Phasor Algebra used in AC Circuits

Figure 1 shows a simple AC series circuit containing resistance and inductance. The sine-wave voltage source causes a sine wave of current to flow in the circuit. Since all the components are connected in series, the current in the inductance and the current in the resistance must have the same …

Read More »## Instantaneous Current in an Ideal Inductor

In the circuit of Figure 1, we assume that the inductor has negligible resistance. To satisfy Kirchhoff’s voltage law, at every instant the inductive voltage across the coil in Figure 1 must exactly equal the applied voltage. Hence, \[{{v}_{L}}=e={{E}_{m}}\sin \omega t \] Figure 1 Inductance in an ac circuit If …

Read More »## Instantaneous Current in a Capacitor

If we connect a capacitor across a sine-wave voltage source, as in Figure 1, Kirchhoff’s voltage law requires the voltage across the capacitor to be exactly the same as the applied voltage at every instant. The voltage across a capacitor can change only if the capacitor charges or discharges. Consequently, …

Read More »## Periodic Wave

Although the sine wave is by far the most important AC waveform, there are many other types of periodic waves. In electric circuits, a periodic wave is any time-varying quantity, such as voltage, current, or power that continually repeats exactly the same sequence of values with each cycle taking exactly …

Read More »## RMS Value of a Sine Wave

All electric circuits convert electric energy into some other form of energy, such as heat, light, or mechanical energy. For many of these energy conversions, it does not matter whether the energy source for the circuit produces direct current or alternating current. Therefore, we find equivalent steady-state values for alternating …

Read More »## Energy Stored in an Inductor

If we connect an ideal inductor to a voltage source having no internal resistance, the voltage across the inductance must remain equal to the applied voltage. Therefore, the current rises at a constant rate, as shown in Figure 1(b). The source supplies electrical energy to the ideal inductor at the …

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