Fig. 24-4 General dc.

direction and again reduces to zero.

As shown graphically in Figure 24-5, plotted, the shape of ac flow is that of a wave. The common ac wave shape is the sine wave. The complete pattern of zero to maximum positive, to zero, down to maximum negative and back to zero is termed a cycle. The time needed to complete one cycle is termed the period of the wave.

The three basic circuit elements, or types of load, that compose an ac electric circuit are: resistance, inductance, and capacitance. Resistance consumes real power, while inductors and capacitors are reactive elements that only store and discharge energy.

Resistance (R) in a circuit is any element that consumes real power in the form of heat. R, measured in Q, is the friction of the electrons flowing in a conductor. It is a physical property of the conductor wire used in a distribution system and results in a loss of power. Resistance causes a voltage drop in conductors and power-using devices. Power loss in a conductor from resistance is equal to the product of the current squared times the resistance of the conductor. The power loss, which is manifest as heat, is the limiting factor for allowable current.

The flow of electric current is similar to the flow of fluid in a pipe. Voltage is like the operating pressure, amperage the flow rate, and resistance the friction. The resistance to current flow is similar to the friction that impedes the flow of the fluid. Like friction, resistance generates heat when current flows through substances. In some cases, such as resistance heating, this phenomenon is advantageous as it provides a useful output.

Conductors are materials, such as copper, that have a very low value of resistance to current flow, thus generating a minimum of heat (power loss). Resistors are materials that conduct current, but have a significant value of resistance to current flow. They generate considerable quantities of heat energy.

Resistance is expressed as:


R = Resistance in ohms

E = Voltage in volts

P = Power in watts

I = Current in amperes

Power loss due to resistance is expressed as:

Power Loss (Watts) = Current2 x Resistance = I2R (24-4)

In accordance with Ohm's Law (I = E/R), the greater the resistance, the lower the current flow. For example, in a basic dc circuit with a 5 ohm resistor, the supply of 10 V will result in a current flow of 2 amps (2 = 10/5). If the voltage across the circuit is reduced to 0 (the circuit is open), then the current flow will be 0. If the voltage is doubled to 20, the current flow will be doubled to 4 amps.

Fig. 24-4 General dc.

In any given circuit, resistance is usually given in a measurement of ohms per foot (meter) for the material and size of the conductor. It is measured as the length of the conductor times the resistance per foot (meter). In many cases, the effects of resistance are relatively minor. However, at large sites with long-load leads, resistance can result in a significant reduction in voltage — or line voltage drop — that can seriously affect the performance of the electrical devices comprising the load.

Actual drop in voltage because of the resistance of the conductors is directly proportional to current flow (E = IR). Voltage drop will be maximum at full load and minimum at no load. In order to compensate for voltage drop, upstream voltage can be increased to a level that will result in the desired voltage at the load-drawing devices.

Inductance occurs when a circuit is closed, current starts to flow in a conductor coil, and lines of magnetic flux establish a magnetic field around the coil. Until the current flow has reached full load and established a complete field, the flux lines are cut by the turns in the conductor, inducing a current in the coil itself. When a circuit is opened, the opposite action occurs. For a brief period after the current flow ceases, the field is still in the process of collapsing. During this period, flux lines again cut the conductors and current is induced in the coil until the field is fully collapsed.

In a dc circuit, induction of current in the coil only occurs when power is being applied or removed. When current flow is constant, there is no increase or decrease in the magnetic field to cause induction of current in the coil.

In an ac circuit, inductance can be of great significance. The flow of current, in a wave form, is constantly changing direction and magnitude. This means that a magnetic field is constantly in the process of forming or collapsing. When a coil is part of an ac circuit, current is always being induced in the coil as long as the circuit is receiving power.

The two factors that affect induction of current in a coil are (a) the number of turns of conductor wire in the coil and (b) the number of lines of magnetic flux being cut per unit time. This rate of change of current flow is affected by the peak value of current in the coil and the frequency (number of complete electric rotations per second, generally 60 or 50 Hz) of the ac applied to the device.

In an ac circuit, as current rises in the cycle, the magnetic field grows stronger with more and more energy being stored in the form of magnetism. As current decreases in the cycle, the magnetic energy returns to the circuit and works to prevent the change in current that produced the magnetism.

An inductor in a circuit creates a hindrance to current flow because the induced current opposes the flow of current. This is called inductive reactance and forms a type of inertia that causes the magnetizing current to be out of phase with the driving voltage. Inductance causes the magnetic field current to lag behind the driving voltage and produces an effective loss of apparent power.

In an ac circuit with a purely inductive load imposed on it, voltage is at peak value when current is at zero, and voltage is at zero when current is at peak value. During the second and fourth quarters of the cycle, the voltage and current waves are of opposite sign (polarity). The zero point of current occurs 90 degrees after the zero point of voltage: the current wave lags the voltage wave by exactly 90 degrees. Inductive loads are, therefore, referred to as lagging loads.

Inductive reactance (XL) is measured in ohms. While voltage across a resistance is equal to current times the resistance (E = IR), voltage across an inductor is equal to the current times the inductive reactance (E = IXL). Inductive reactance, like resistance, tends to limit the magnitude of current flow in an ac circuit. For any given voltage across an inductance, the higher the XL, the lower the current flow. Unlike resistance, however, Xl varies directly with frequency. If, for example, at constant voltage, frequency is reduced from 60 Hz to 50 Hz, the current flow will increase to 120% of the value at 60 Hz.

Capacitance is a quantity that defines the ability of a capacitor — or electron collector — to hold a charge. While inductance is related to current and magnetism, capacitance is related to voltage. Capacitors, sometimes referred to as condensers, are circuit elements that have the ability to store up an electric charge. Its capacity is a function of the areas of the conducting plates, the thickness of the insulating material, and the impressed voltage. With an inductance in a dc circuit, voltage is induced only when there is a change in current flow. With a capacitor, however, current will only flow when there is a change in voltage.

Inductance and capacitance both occur only when there is a change in rate of current flow and in voltage, respectively. Capacitance, thus, has the same significance as inductance in an ac circuit.

In an ac circuit, both capacitance and inductance hinder current flow. However, while inductance hinders flow by opposing it, capacitance hinders flow by storing it. Capacitive reactance (XC), measured in ohms, is the hindrance to current caused by the presence of capacitance in an ac circuit. The voltage across a capacitor in an ac circuit is equal to the current times the capacitive reactance (E = IXc).

As voltage rises in the cycle, greater volumes of electrons are impressed and stored on the plates of a capacitor up to the peak voltage. As voltage drops (the second quarter of the first half of the sine wave), the electrons are returned to the circuit. As voltage changes polarity (second half of the sine wave), the electron charges on the plates change polarity and work to prevent a change in the voltage.

This forms a type of inertia, causing the voltage to be out of phase with, and lag behind, the current. It is the opposite effect of inductance and causes an equally effective loss of apparent power. A leading current is the current flowing in a circuit that is mostly capacitive. If a circuit contains only capacitance, the current leads the driving voltage by 90°. Figure 24-6 shows a plot of voltage versus current for both a pure capacitance circuit and a pure inductance circuit.

Fig. 24-6 Plot of Voltage vs. Current. Where:

Ic = Current for purely capacitive circuit Il = Current for purely inductive circuit E = Voltage

Capacitive reactance depends on rate of voltage change, in volts per second. Like inductive reactance, capacitive reactance is affected by frequency and tends to limit the magnitude of current flow. That is, the greater the capacitive reactance, the lower the magnitude of current flow. The critical difference is that while inductive reactance is directly proportional to frequency, capacitive reactance is inversely proportional to frequency. If frequency is increased, the value of capacitive reactance is reduced. For example, if the frequency in an ac circuit containing capacitive reactance is increased from 50 Hz to 60 Hz, the magnitude of current flow will increase by 120% of the 50 Hz value.

Impedance (Z) is the sum of total hindrance to current flow. The equation for impedance, measured in ohms, is:

Impedance is the total opposition or hindrance (resistance and reactance) of a circuit to the flow of alternating current at a given frequency. In alternating current, voltage drop in a conductor is equal to current times impedance. In direct current, since there is no effect of capacitance and inductance, voltage drop is equal to current times resistance.

There is always some amount of resistance in all circuits. In ac circuits, one or both of the other circuit elements — inductive and capacitive reactance — are often present. Impedance in an ac circuit, therefore, is a function of one or more of the following equations, depending on the circuit elements involved:

Inductive elements: E = IXl (24-7)

Capacitive elements: E = IXc (24-8)

To calculate the total hindrance to current flow in a circuit, the opposite (offsetting) effects of Xl and Xc must be considered. The relevant factor is the net effect of these two phenomena. To obtain the net total of these two reactances, one is subtracted from the other. With resistance, inductance, and capacitance in series, the equation for impedance is:

In ac circuits, where resistance is only one of three possible forms of hindrance to current flow, Z must be substituted for R to validate Ohm's Law. The formula of E = IR, therefore, becomes E = IZ.

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