1.5. Quality and standardization 1 Quality 1 Quality
2.1.2 Alternating current (AC)
An electric current that reverses its direction of flow at regular intervals is called an alternating current (AC). The AC circuits are of major importance in applied electricity. The alternating current is positive as much as it is negative. A typical sine wave showing AC voltage is shown in FIG. 2.2 below. Alternating voltage periodically reverses in polarity, causing alternating current that periodically reverses its direction.
FIG. 2.2. Sine wave curve showing AC voltage.
Amplitude and Phase
The systems that vary periodically with time are called sinusoidal time variation systems.
Electric circuits tend to develop sinusoidally varying currents and voltages, or have particularly simple responses to sinusoidal signals. To maintain a continuous current in a conductor, the electric field has to be maintained i.e. the potential difference across the conductor has to be maintained. If the field reverses its direction periodically, the flow of charge reverses and the current is thus alternating between the two constant maximum positive and maximum negative values. This is illustrated in FIG. 2.3. The maximum vertical height of the wave is called its amplitude. The voltage changes its amplitude every half cycle and an equal time to reach maximum of negative amplitude value.
The time taken to complete one cycle is termed as the time period and the number of cycles per second is called the frequency. The unit of frequency is Hertz (Hz), which is equal to 1 cycle per second. In the sine wave curve shown above along the X axis we have phase angle in radians or degrees, whereas Y axis represent the amplitude at a particular time. At π/2 or 90
° we have the maximum positive amplitude of the wave form, while at 3π/2 or 270° we have maximum negative amplitude of the wave form. The angle subtended by any point of the curve to its initial position is called as the phase angle. At any time t the instantaneous voltage V (t) is given by
) 2 sin(
sin )
(t V0 t V0 ft
V = ω = π , (2.7)
where
V(t) = instantaneous voltage V0 = initial voltage
ω = angular frequency t = time
f = frequency
FIG. 2.3. Voltage and current in phase.
FIG. 2.4.a. Current leading voltage by 90°. FIG. 2.4.b. Current lagging voltage by 90°.
Phase angles
Although the sine wave shown in FIG. 2.2 can be used to represent either the current or the voltage, if both current and voltage are to be shown then two sine waves are required. When the sine waves of the current and the voltage both pass through zero in the same direction and at the same time, then the voltage and current are said to be in phase with each other, as shown in FIG. 2.3. However, as will be discussed later, the current and voltage may not be in phase with one another. The current may lead or lag the voltage. The amount by which the current leads or lags can be expressed in degrees or time as shown in FIG. 2.4.
Effect of pure resistance
When an alternating current is passed through a pure resistance the current can be calculated by dividing the voltage by the resistance. As the resistance remains constant, the current is proportional to the voltage. As the voltage is continually changing, in both strength and direc-tion, the current will change in a similar manner. Therefore, the voltage and current curves will rise and fall together as shown in FIG. 2.5 and are said to be `in phase’ at the same frequency. However, as the value of the resistance affects the current flow, the amplitudes of the voltage and current may be different in accordance with Ohms Law. The value of resistance is not affected by a change in frequency.
Voltage Current
C urrent
Voltage
V oltage
C urrent
FIG. 2.5. Circuit having pure resistance.
Effect of pure inductance
Inductance, like resistance, imposes a limit on the current which a given ac voltage will cause to flow in a circuit. The magnitude of opposition to current flow by an inductance is called inductive reactance (XL), which, unlike resistance, varies with frequency. If the frequency is zero (dc), there is no inductance and a coil will act as an ordinary conductor, but as frequency increases (ac), the rate of change of the coil magnetic field increases and the coil will become more and more inductive, thereby increasing the opposition to current flow. Therefore the higher the frequency, the higher the inductive reactance. As inductance is a magnetic property dependent on the rate of change of the current, in a purely inductive circuit (where it is assumed there is no resistance), the current will lag the voltage by 90° as shown in FIG. 2.6.
This is further explained by appreciating that the magnetic field is changing in each cycle at its maximum rate of change when the voltage is zero. As the voltage passes through zero on each cycle, the induced (opposite) EMF is a maximum. Inductive reactance, like resistance, is measured in Ohms.
XL = 2πfL (2.8)
Where XL =inductive reactance f = frequency
L = inductance
FIG 2.6. Circuit having pure inductance.
Voltage Current
Voltage and Current in Phase Resistance
(R)
Voltage
Current
Current lags Voltage by 90°
Inductance (L)
Effect of pure capacitance
In a dc circuit, a fully charged capacitor acts as a complete break and no current will flow.
However, in an ac circuit the capacitor is continually being charged and discharged as the voltage alternates. As can be seen in FIG. 2.7, when the voltage is at its maximum value the capacitor is fully charged and no current will flow. When the voltage falls the capacitor discharges and the current will be at its maximum value when the voltage is zero. As the voltage increases again, the current will decrease and so on. Therefore, in a purely capacitive circuit (where it is assumed there is no resistance), the current will lead the voltage by 90°.
One can consider the analogy of a hydraulic accumulator being charged and discharged. As the pump starts and the accumulator is empty the flow is maximum with minimum pressure.
Capacitance, like resistance and inductance, imposes a limit on the current which a given ac voltage will cause to flow in a circuit. The magnitude of opposition to current flow by a ca-pacitance is called capacitive reactance (XC) and is measured in Ohms. Capacitive reactance also varies with frequency but unlike inductive reactance, the higher the frequency, the lower the capacitive reactance.
XC = 1 (2.9)
2πfC where
Xc = capacitive reactance f = frequency
C = capacitance
FIG. 2.7. Circuit having pure capacitance.
Resonant frequency
If a circuit contains an inductor and a capacitor and the value of inductive reactance and capacitive reactance are equal the circuit is said to be in resonance (XL = XC). Because the value of both XL and XC are both frequency dependent, it can be seen that resonance will always occur at a fixed frequency dependent on the values of impedance and capacitance.
Voltage
Current leads Voltage by 90°
Capacitance (C)
Current
Impedance
In the circuit shown in FIG. 2.8, the opposition to current flow is due not only to resistance but also to inductive and capacitive reactance. This total opposition is called impedance (Z). If the resistance, inductive reactance and capacitive reactance are drawn vectorially with magnitude and direction and with a horizontal line representing zero phase angle, then the resistance will be drawn as a horizontal line whose length is proportional to its magnitude. As an inductance causes a phase lag of 90°, the inductive reactance can be drawn as a vertical line upwards whose length is proportional to its magnitude. Similarly, as a capacitance causes a phase lead of 90°, capacitance reactance can be drawn as a vertical line downwards as shown in FIG 2.9.
A simplified representation of the 3 component parts of an alternating circuit is shown in FIG.
2.10. below. The inductive reactance and the capacitive reactance are in opposition to each
The impedance and the phase angle of the current caused by the voltage applied to the impedance can be calculated using right angle triangle calculations (Pythagoras). The impedance amplitude can be determined using the formula:
Z = R2 + (XC - XL)2 (2.10)
where
Z = impedance R = resistance
Xc = capacitive reactance XL = inductive reactance
Similarly, the phase angle can be determined using trigonometry with the formula:
θ° = tan-1 (XC – XL) (2.11)
R
where
θ° = phase angle
Xc = capacitive reactance XL = inductive reactance R = resistance
As both the inductive reactance and capacitive reactance vary with frequency, any variation in frequency will change the impedance and phase angle.
If XL is greater than XC then the impedance Z has a lagging phase angle and the circuit is inductive.
If XC is greater than XL then the impedance Z has a leading phase angle and the circuit is capacitive.
If XL = XC then the phase angle is zero. Then Z = R therefore the circuit is resistive only.2.2. Magnetism
Magnetism is a property possessed by certain material by which this material can exert a mechanical force of attraction and repulsion on other like materials. The most well known example of the effects of magnetism is the attraction that the magnet has for an iron nail.
Magnetic materials
If an object is placed in a magnetic field a force is exerted on it and it becomes magnetized.
The intensity of magnetization depends upon the susceptibility of the metal to become magnetized. Some metals are attracted to a magnet, these are para-magnetic metals of which ferro-magnetic materials are a sub group. Others are repelled by magnets; these are dia-magnetic metals. An illustration of these relationships is shown in FIG. 2.11.
Para-magnetic materials
Para-magnetic metals have a positive susceptibility to magnetization that means they are attracted to magnets. Some are only weakly attracted; magnesium, molybdenum, lithium and
DIAMAGNETIC µ < 1 NON MAGNETIC µ = 1
µ > 1 PARAMAGNETIC µ >> 1
FERROMAGNETIC B
H
FIG. 2.11. Ferro-, para-, dia- and non-magnetic permeability relationships.
Ferromagnetic metals
These are para-magnetic materials that have a large and positive susceptibility to magnetization. They have a strong attraction and are able to retain their magnetization after the magnetizing field has been removed. Iron, cobalt and nickel are examples of ferromagnetic metals.
Ferromagnetic materials are the only metals commonly inspected with the magnetic particle testing method. This includes welded steel structures and nickel based jet turbine blades.
Dia-magnetic materials
Diamagnetic metals have a small and negative susceptibility to magnetization or are slightly repelled by magnets. Copper, silver and gold are examples of diamagnetic materials.