Electric current and quantity of electricity

All atoms consist of protons, neutrons and electrons. The protons, which have positive electrical charges, and the neutrons, which have no electrical charge, are contained within the nucleus. Removed from the nucleus are minute negatively charged particles called electrons. Atoms of different materials differ from one another by having different numbers of protons, neutrons and electrons. An equal number of protons and electrons exist within an atom and it is said to be electrically balanced, as the positive and negative charges cancel each other out. When there are more than two electrons in an atom the electrons are arranged into shells at various distances from the nucleus.

All atoms are bound together by powerful forces of attraction existing between the nucleus and its electrons. Electrons in the outer shell of an atom, however, are attracted to their nucleus less powerfully than are electrons whose shells are nearer the nucleus.

It is possible for an atom to lose an electron; the atom, which is now called an ion, is not now electrically balanced, but is positively charged and is thus able to attract an electron to itself from another atom. Electrons that move from one atom to another are called free electrons and such random motion can continue indefinitely. However, if an electric pressure or voltage is applied across any material there is a tendency for electrons to move in a particular direction. This movement of free electrons, known as drift, constitutes an electric current flow. Thus current is the rate of movement of charge.

Basic electrical measuring instruments

An ammeter is an instrument used to measure current and must be connected in series with the circuit. Figure 2.2 shows an ammeter connected in series with the lamp to measure the current flowing through it. Since all the current in the circuit passes through the ammeter it must have a very low resistance.

A voltmeter is an instrument used to measure p.d. and must be connected in parallel with the part of the circuit whose p.d. is required. In Figure 2.2, a voltmeter is connected in parallel with the lamp to measure the p.d. across it. To avoid a significant current flowing through it a voltmeter must have a very high resistance.

Power factor improvement

For a particular active power supplied, a high power factor reduces the current flowing in a supply system and therefore reduces the cost of cables, transformers, switchgear and generators, as mentioned in Section 16.7, page 252. Supply authorities use tariffs which encourage consumers to operate at a reasonably high power factor. One method of improving the power factor of an inductive load is to connect a bank of capacitors in parallel with the load. Capacitors are rated in reactive voltamperes and the effect of the capacitors is to reduce the reactive power of the system without changing the active power. Most residential and industrial loads on a power system are inductive, i.e. they operate at a lagging power factor. A simplified circuit diagram is shown in Figure 26.11(a) where a capac- itor C is connected across an inductive load. Before the capacitor is connected the circuit current is ILR and is shown lagging voltage V by angle 1 in the phasor diagram of Figure 26.11(b). When the capacitor C is connected it takes a current IC which is shown in the phasor diagram leading voltage V by 90°. The supply current I in Figure 26.11(a) is now the phasor sum of currents ILR and IC as shown in Figure 26.11(b). The circuit phase angle, i.e., the angle between V and I, has been reduced from 1 to 2 and the power factor has been improved from cos 1 to cos 2. Figure 26.12(a) shows the power triangle for an inductive circuit with a lagging power factor of cos 1. In Figure 26.12(b), the angle 1 has been reduced to 2, i.e., the power factor has been improved from cos 1 to cos 2 by introducing leading reactive voltamperes (shown as length ab) which is achieved by connecting capacitance in parallel with

the inductive load. The power factor has been improved by reducing the reactive voltamperes; the active power P has remained unaffected. Power factor correction results in the apparent power S decreasing (from 0a to 0b in Figure 26.12(b)) and thus the current decreasing, so that the power distribution system is used more efficiently. Another method of power factor improvement, besides the use of static capacitors, is by using synchronous motors; such machines can be made to operate at leading power factors.

Series resonance

When the voltage V applied to an electrical network containing resistance, inductance and capacitance is in phase with the resulting current I, the circuit is said to be resonant. The phenomenon of resonance is of great value in all branches of radio, television and communications engineering, since it enables small portions of the communications frequency spectrum to be selected for amplification independently of the remainder. At resonance, the equivalent network impedance Z is purely resistive since the supply voltage and current are in phase. The power factor of a resonant network is unity,(i.e., power factor D cos D cos 0 D 1). In electrical work there are two types of resonance— one associated with series circuits,(which was introduced in Chapter 15), when the input impedance is a minimum, (which is discussed further in this chapter), and the other associated with simple parallel networks, when the input impedance is a maximum (which is discussed in Chapter 29).

In an L–C–R circuit both of the reactive elements store energy during a quarter cycle of the alternating supply input and return it to the circuit source during the following quarter cycle. An inductor stores energy in its magnetic field, then transfers it to the electric field of the capacitor and then back to the magnetic field, and so on. Thus the inductive and capacitive elements transfer energy from one to the other successively with the source of supply ideally providing no additional energy at all. Practical reactors both store and dissipate energy. Q-factor is an abbreviation for quality factor and refers to the ‘good- ness’ of a reactive component.

Q-factor in a parallel network

The Q-factor in the series R–L–C circuit is a measure of the voltage magnification. In a parallel circuit, currents higher than the supply current can circulate within the parallel branches of a parallel resonant network, the current leaving the capacitor and establishing the magnetic field of the inductance, this then collapsing and recharging the capacitor, and so on. The Q-factor of a parallel resonant circuit is the ratio of the current circulating in the parallel branches of the circuit to the supply current, i.e. in a parallel circuit, Q-factor is a measure of the current magnification. Circulating currents may be several hundreds of times greater than the supply current at resonance. For the parallel network of Figure 29.5, the Q-factor at resonance is given by:

the same expression as for series resonance. The difference between the resonant frequency of a series circuit and that of a parallel circuit can be quite small. The resonant frequency of a coil in parallel with a capacitor is shown in Equation (29.3); however, around the closed loop comprising the coil and capacitor the energy would naturally resonate at a frequency given by that for a series R–L–C circuit, as shown in Chapter 28. This latter frequency is termed the natural frequency, fn , and the frequency of resonance seen at the terminals of Figure 29.5 is often called the forced resonant frequency, fr. (For a series circuit, the forced and natural frequencies coincide.)

Mesh-current and nodal analysis

Mesh-current analysis is merely an extension of the use of Kirchhoff’s laws, explained in Chapter 30. Figure 31.1 shows a network whose circu- lating currents I1, I2 and I3 have been assigned to closed loops in the circuit rather than to branches. Currents I1, I2 and I3 are called mesh- currents or loop-currents.

In mesh-current analysis the loop-currents are all arranged to circu- late in the same direction (in Figure 31.1, shown as clockwise direction). Kirchhoff’s second law is applied to each of the loops in turn, which in the circuit of Figure 31.1 produces three equations in three unknowns which may be solved for I1, I2 and I3. The three equations produced from Figure 31.1 are:

Aurther

John Bird

Downlaod Book