Lecture 4: Introduction to DC Generator PDF

Lecture 4: Introduction to DC generator, resistors, Series and Parallel Circuits connections. Introduction to the DC generator A direct current (DC) generator is another device that produces a potential difference. A DC generator is an electrical machine whose m...

Lecture 4: Introduction to DC generator, resistors, Series and Parallel Circuits connections. Introduction to the DC generator A direct current (DC) generator is another device that produces a potential difference. A DC generator is an electrical machine whose main function is to convert mechanical energy into electricity. What is the principle of a DC generator? A DC generator works on the principle of electromagnetic induction of Faraday’s Laws. How Does a DC Generator Work? According to Faraday’s law of electromagnetic induction, an electromagnetic field (EMF) is induced in a conductor when the conductor is placed in a varying magnetic field. According to Fleming’s right-hand rule, the direction of the induced current changes whenever the direction of motion of the conductor changes. Let us consider an armature rotating clockwise and a conductor at the left moving upwards. When the armature completes a half rotation, the direction of the motion of the conductor will be reversed downward. Hence, the direction of the current in every armature will be alternating. But in the D.C. generator the output from the rotor assembly is fed to a commutator. The current in the commutator alternates direction, just as it does in the coil. However, the rate of this alternation matches the rate at which the commutator switches electrical contact with either end of the external circuit (brushes). The net effect is that even though the current in the coil continues to alternate, the current in the external circuit always points in the same direction. By this means, the commutator rectifies current. We now consider the rectified current produced by one complete revolution of the rotating coil. The magnitude of the current generated depends on the angle of the coil with respect to the magnetic field. We can say that initially, the coil has the following position. In this orientation, the coil produces no current. This is always true when the coil lies in a plane perpendicular to the magnetic field. The coil turning through other angles, however, generates current that is then rectified by the commutator. Note the orientations of the coil relative to the field that produce minimum and maximum currents.  The rectified current delivered to the external circuit over one full rotation of the coil is shown in the following figure. Therefore, we get a unidirectional current at the terminals when the conductor circuit is closed. One of the most common examples of a DC generator is the generator in a car which is used to recharge the battery. DC Generator construction 1) Stator The main function of the stator is to provide magnetic fields where the coil spins. A stator includes two magnets with opposite polarities facing each other. These magnets are located to fit in the region of the rotor. 2) Armature Windings The armature is a rotating part of a DC generator, consisting essentially of copper wire wound around an iron core. 3) Commutator The commutator is a ring split into equal halves (Split rings), with each half insulated and linked to opposite ends of the rotating coil. Each end of the rotating coil is fixed to one half of the split ring commutator. As the coil and commutator rotate together, electrical contact with the external circuit is maintained by what are called brushes. For one-half of a rotation, it will contact one brush, and for the other half, it will contact the second brush. The commutator is responsible for producing pulsating DC voltage and current. The commutator assures that the current from the generator always flows in one direction. To minimize this pulsating effect, additional poles, armature coils, and commutator segments are added. 4) Brushes The purpose of the brushes is to make electrical contact with a rotating conductor (the commutator), and it facilitates the flow of current to the connected load, ensuring that the coil permits current to exit in just one direction. Brushes are in contact with split rings whenever generator is running. Due to friction action, arcing and sparking is an unavoidable characteristic of the machine at the brush interface. Electrical arcs produce very high temperatures. High enough to melt metals. Types of brushes are carbon, graphite, mixture of carbon and copper. It is common to use assorted types of graphite. Early machines used brushes made from strands of copper wire to contact the surface of the commutator. However, these hard metal brushes tended to scratch and groove the smooth commutator segments, eventually requiring resurfacing of the commutator. Sparks yellow in color indicate that these are caused due to uneven surface of the commutator. As the copper brushes wore away, the dust and pieces of the brush could wedge between commutator segments, shorting them and reducing the efficiency of the device. Brushes made with copper or steel would wear out faster because of factors including: 1) The melted metal will break away from, or even be vaporized, leaving the brush with less material to do its job. 2) If the melted material doesn't vaporize or otherwise move away from the interface, it creates a mess for the brush. It can weld together bristles of the brush. It can build up material that interferes with the motion of the rotor. 3) As the metal melts in the presence of an arc, conductive material can be liberated, therby prolonging the arc, exasperating the wearing action. Carbon brushes are made from Carbon metal that has a melting point that is often greater than that of copper and other common metals. Carbon brushes have a melting temperature of 3550 degrees Celsius, while copper has a melting point of just 1080 degrees Celsius. Carbon brushes have self-lubricating properties, they are softer than copper, the soft carbon causes far less damage to the commutator, and Carbon will acquire the shape of the commutator segments and, so, will ensure maximum contact with commutator segments. Carbon brushes tend to be worn more evenly than copper brushes. There are less sparks with carbon as compared to copper, but as the carbon wears away, fewer problems from the dust collecting on the commutator segments. In that way, the easily replaced brushes are worn away rather than the much harder to replace copper alloy commutator. Worn out brushes also cause sparking on the commutator. Carbon brushes that will gradually become worn during use and may need to be replaced. If the carbon brushes in your machine have reduced to about a quarter of their original size, they should be discarded, and new ones should be installed. There is an engraved line on each carbon brush which indicates the limit up to which the brush could be used. Graphite is a crystalline form of carbon. Graphite is conductive and auto-lubricant (low friction coefficient). So, it provides good dynamic contact to rings with minimum erosion because it absorbs heat without undergoing melting. So, the heat will be dissipated by the graphite more efficiently and effectively. Therefore, either carbon / graphite is used for making the brushes. Brush Springs The efficiency of a generator largely depends on the quality of the connection between the brushes and the commutator. A firm, steady pressure is required for a consistent electrical connection. That’s where brush springs come into play. They provide the necessary force that keeps the brushes in constant contact with the commutator, facilitating continuous current transfer and preventing arcing and pitting. brush springs are typically made from high-grade spring steel. This type of steel is specifically designed to withstand the constant stress and tension that comes with the continuous operation of electric generators. The materials must be both robust and flexible, providing consistent force without deforming or breaking over time. Spring pressure a) Low pressure on the carbon brushes…. Inadequate spring tension can also cause brushes to jump easily which reflects in sparking. Pulling the lead of a carbon brush by hand up to one or two centimeters and releasing it could give an idea if spring has lost its tension. Comparative checking with other brushes can point out a defective spring. Replace the defective spring can help solve this problem. b) It could be spring pressure causing one brush to wear faster. Efficiency of Brushes The wearing of both brushes and commutators is a disadvantage of a DC generator. Thus, they are less efficient, because sparking and short circuit possibility being high. So, DC generators require frequent maintenance and replacement are needed to operate properly. Why are they worn out easily? Because it will produce electric sparks each time the commutator and brushes connect with each other.  Passive Circuit Elements Circuit Loads A load generally refers to a component or a piece of equipment connected to the output of an electric circuit. In its fundamental form, the load is represented by any one or a combination of the following: 1. Resistor (R) 2. Inductor (L) 3. Capacitor (C) A load can either be of resistive, inductive or capacitive nature or a blend of them. For example, a light bulb is a purely resistive load whereas a transformer is both inductive and resistive. A circuit load can also be referred to as a sink since it dissipates energy whereas the voltage or current supply can be termed as a source. Table 2.2 shows the basic circuit elements along with their symbols and schematics used in an electric circuit. The R, L and C are all passive components i.e. they do not generate their own emf whereas the DC voltage and current sources are active elements. Table: Common circuit elements and their representation in an electric circuit. Resistor Resistors are important in electronic circuits because they allow for the control of current flow. Some substances, such as carbon, conduct electricity fairly well but not really well. The conductivity can be changed by adding impurities. Electrical components made in this way are called resistors. The resistive element in carbon composition resistors is made from a mixture of finely powdered carbon and an insulating material, usually ceramic. The resistance is determined by the ratio of the fill material (the ceramic) to the carbon. Resistors can be manufactured to have exact characteristics. Imagine telling each person in the line that they must pass a certain number of balls per minute. This is analogous to creating a resistor with a certain value of electrical resistance. The better a resistor conducts, the lower its resistance; conversely, the worse it conducts, the higher the resistance. Electrical resistance is measured in units called ohms. The higher the value in ohms, the greater the resistance, and the more difficult it becomes for current to flow. The resistance converts electrical energy into heat. For wires, the resistance is sometimes specified in terms of ohms per foot or ohms per kilometer. In an electrical system, it is usually desirable to have as low a resistance, or ohmic value, as possible. This is because resistance converts electrical energy into heat. To describe the resistance of a resistor and hence its characteristics, it is important to define the Ohm’s law. Ohm's Law. Ohm's law states that the voltage and current in a resistor are directly proportional. Resistors that obey the Ohm's law are called linear or ohmic resistors. In an ohmic resistor the ratio of the resistor voltage to the resistor current is independent of the voltage and current. This ratio is defined as the resistance of the resistor, and it is measured in Ω (Ohms). Equation (1) expresses the Ohm's law. This equation is the terminal equation of a linear resistor. V =R. I (1) Equation (1) can also be written as in (2): I= G. V (2) Where G=1/R is the conductance of the resistor (measured in Siemens, S). Representation of the terminal equation of a resistor in the form of (1) is called resistance or impedance representation. Representation in the form of (2) is called conductance or admittance representation. Resistors whose resistance varies with the voltage or the current in the resistor are called nonlinear resistors. Non-linear resistors are described by a non-linear relation between their voltage and current. The Voltage versus Current Characteristic of Linear Resistors. The graph of the voltage v. the current of a linear resistor is a line called the V-I characteristic. With reference to Figure A, the V-I characteristic of the resistor always passes through the origin. Its slope is the resistance of the resistor. Its reciprocal slope is the conductance of the resistor. An ohmic resistor characteristic occupies only the first and third quadrant of the V-I plane. Thus, an ohmic resistor dissipates energy at any point of its characteristic.  Fig. A. The V-I characteristic of a linear resistor. Series and Parallel Circuit connections There are two fundamental ways in which to connect more than two circuit components: series and parallel. The components in a circuit are joined by wires. These two basic connection methods can be combined to create more complex series-parallel circuits. Series circuit connection (Voltage divider) In a series circuit connection, all components are connected end-to-end to form a single path for current flow. If you follow the circuit diagram from one side of the cell to the other, you should pass through all the different components, one after the other, without any branches. If there are no branches, then it's a series circuit. Figure 1. Series connection of resistors A circuit with a battery and two lamps connected in series Opening or breaking a series circuit at any point causes the entire circuit to "open" or stop operating. In a series circuit, if a lamp breaks or a component is disconnected, the circuit is broken, and all the components stop working. Series circuits are useful if you want a warning that one of the components in the circuit has failed. They also use less wiring than parallel circuits. The current in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current. A series circuit has only one path through which its current can flow. The total voltage is the sum of the voltage through the individual components, in accordance with Kirchoff’s voltage law. Series Combination of Resistors. In a series circuit, the total resistance across all of the components (the 'net resistance') increases as more components are added. The total resistance (RT) for this circuit is R1+R2. RT=R1+R2 The equivalent resistance of resistors connected in series equals the summation of the resistance of each resistor. With reference to Figure B, the equivalent V-I characteristic of series resistors is obtained by the vertical summation of the V-I characteristics of the resistors. The slope of the equivalent characteristic is, thus, the summation of the slopes of each of the added characteristic. Fig. B. The combined V-I characteristic of series resistors. (a) and (b) The V-I characteristics of the resistors. (c) The combined V-I characteristic. To put this equation more generally: the total resistance of N -- some arbitrary number of -- resistors is their total sum. Current in series connection A series circuit’s defining characteristic is that all components in a series circuit have the same current flowing through them. There is only one path for the current to flow. In the circuit, the current (I) flows to complete a full loop from the positive battery terminal back to the negative terminal and then through the battery. A series circuit is one loop: all electrons in that loop form one current. An ammeter will measure the same current wherever it is placed in the circuit, The resistors have the same current through them. If the resistance of any component in a series circuit change, this will change the value of the current in the circuit. 𝑰 = 𝑰𝟏 = 𝑰𝟐 = 𝑰𝟑 current (I) is measured in amps (A) Voltage in series connection The total voltage is the sum of the voltage through the individual components, in accordance with Kirchoff’s voltage law. Kirchoff’s voltage law The principle known as Kirchhoff’s Voltage Law can be stated as such: “The algebraic sum of all voltages in a loop must equal zero” By algebraic, I mean accounting for signs (polarities) as well as magnitudes. By loop, I mean any path traced from one point in a circuit around to other points in that circuit, and finally back to the initial point. Figure 1. Series connection of resistors Here, we have three resistors (labeled R1, R2, and R3) connected in a long chain from one battery terminal to the other. Each resistor in a series circuit shares one electrical node with its nearest neighbor. The supply voltage is shared between components in a series circuit. Since energy has to be conserved, the sum of the voltages across components in series is equal to the voltage of the supply. The voltage across the terminals of a series arrangement is distributed among the resistors proportionally to the resistance of each resistor (voltage division). This means that if two identical components are connected in series, the supply voltage divides equally across them. The potential difference across them will be different if they have different resistances. If you put more lamps into a series circuit, the lamps will be dimmer than before. Vs=V1+V2 potential difference (V) is measured in volts (V) If the resistance of any component in a series circuit change, this will change the potential difference across all of the components. Figure: Voltage divider Potentiometer A potentiometer is a three-terminal resistor with a sliding or rotating contact. It is an adjustable voltage divider with two static contacts and one moving contact. The moving terminal is a wiper that travels across the resistance element, usually in an arc controlled by a rotary knob. Rotating the knob gives a ratiometric division of the potential across the resistance element. Potentiometer generally used in speakers and receivers for volume control. In addition, it cannot directly control the motor because its power is too small. Potentiometer Wiring The potentiometer can be used as a three-terminal component or a two-terminal component. The latter can be regarded as a rheostat. For a general potentiometer (three pins), the slider near the center which is a resistance wire. The two pins at both ends of the resistance wire are connected to the input and the ground (some are not connected), respectively. That is, one pin is connected to the input signal and the other pin is grounded. At this time, the resistance wire has a total resistance value on the two sections. You move the sliding piece to go across this resistance wire to get a variable resistance. If the input and output signals are reversed, the sliding direction of the slide is opposite to the resistance change. Figure 1. Potentiometer Structure 1. Two-terminal component (rheostat). For a potentiometer (or a trimming resistors) with traditional pins (three pins), the resistance at both ends is fixed, and the resistance of the middle pin is variable. That is, the terminal on both sides of the potentiometer is total resistance, and the middle is changing. The rheostat is just a variable resistor with no regard to polarity. For example, the power supply is connected from any one contact on resistor sides and output from the middle contact, and the voltage changes with the rotation of the middle contact. If a potentiometer used as a variable resistor, one end connects to the input voltage, the middle- end connects to the output, and the other end can be suspended or connected to the middle-end to obtain a smooth and continuously changing resistance value. 2- Three-terminal component (variable voltage divider) If a potentiometer used as a variable voltage divider, one contact connects to the input voltage, the middle contact connects to the output voltage, and the other contact can be grounded. When the rotary handle or sliding handle of the potentiometer take action, the movable contact slides on the resistor. At this time, an output voltage that has a certain relationship with the external voltage, wiper angle and travel stroke. Figure. Potentiometer Circuit  Figure. Potentiometer as Voltage Divider Voltage dividers find wide application in electric meter circuits, where specific combinations of series resistors are used to “divide” a voltage into precise proportions as part of a voltage measurement device. One device frequently used as a voltage-dividing component is the potentiometer, which is a resistor with a movable element positioned by a manual knob or lever. This application of the potentiometer is a very useful means of obtaining a variable voltage from a fixed-voltage source such as a battery. If a circuit you’re building requires a certain amount of voltage that is less than the value of an available battery’s voltage, you may connect the outer terminals of a potentiometer across that battery and “dial-up” whatever voltage you need between the potentiometer wiper and one of the outer terminals for use in your circuit:  Figure 3: potentiometer as Voltage divider Parallel circuit connection In a parallel circuit connection, all components are connected across each other with exactly two electrically common nodes with the same voltage across each component. If there are branches, it's a parallel circuit. If two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchoff’s current law. Parallel Combination of Resistors. The equivalent conductance of resistors connected in parallel equals the summation of the conductance of each resistor. With reference to Figure C, the V-I characteristic of the parallel combination of resistors is obtained by the horizontal summation of the V-I characteristics of the resistors. The reciprocal slope of the V-I characteristic of parallel resistors is the summation of the reciprocal slopes of the V-I characteristics of the resistors. Fig. C. The combined V-I characteristic of parallel resistors. (a) and (b) The V-I characteristics of the resistors. (c) The combined V-I characteristic. Parallel resistors divide the current at the terminals of the arrangement proportionally to their conductance (current division). Ohm’s Law It is the most fundamental law used in circuit analysis. It provides a simple formula describing the voltage-current relationship in a conducting material. Statement The voltage or potential difference across a conducting material is directly proportional to the current flowing through the material. Mathematically Figure 2.5. where the constant of proportionality R is called the resistance or electrical resistance, measured in ohms (Ω). Graphically, the V-I relationship for a resistor according to Ohm’s law is depicted in Figure 2.5. Figure 2.5: V-I relationship for a resistor according to Ohm’s law. At any given point in the above graph, the ratio of voltage to current is always constant. Example Find R if the voltage V and current I in Figure 2.5 are equal to 10 V and 5 A respectively. V =10V, I = 5 A, R =? V = IR or R = V/I=10/5 ∴ R =2Ω A short circuit between two points represents a zero resistance whereas an open circuit corresponds to an infinite resistance as demonstrated in Figure 2.6. Parallel Connection (current divider) In a parallel circuit, all components are connected across each other with exactly two electrically common nodes with the same voltage across each component as shown in Figure. Parallel circuit is often called a current divider for its ability to proportion or divide the total current into fractional parts. If two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s Current Law. Kirchhoff’s Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.” This law is used to describe how a charge enters and leaves a wire junction point or node on a wire. Mathematically, we can express this general relationship as such: Figure: An example of a parallel connection of resistors. In a parallel circuit, the net resistance decreases as more components are added, because there are more paths for the current to pass through. The two resistors have the same potential difference across them. The current through them will be different if they have different resistances. The total current in the circuit is the sum of the currents through each branch. There are many paths for current flow, but only one voltage across all components. Again, we have three resistors, but this time there are three loops for the current to flow from the positive battery terminal back to the negative terminal: 1. 1–2–7–8–1 2. 1–2–3–6–7–8–1  3. 1–2–3–4–5–6–7–8–1 Each individual path through R1, R2, and R3 (2–7, 3–6, and 4–5) is called a branch. A parallel circuit’s defining characteristic is that all components are connected between the same set of electrically common points. Looking at the schematic diagram from Figure 4, we see those points 1, 2, 3, and 4 are all electrically common; so are points 5, 6, 7, and 8. All of the resistors, as well as the battery, are connected between these two sets of points. This means that the same voltage (V) is dropped across all components in a parallel circuit. An example of current divider IR2+IR3-(IR2+IR3)=0 Connecting components in parallel When we connect components in parallel, the components are connected on different branches of the circuit. There are two or more 'loops’ and multiple paths for a current to flow. In a parallel circuit, if a lamp breaks or a component is disconnected, the other components continue working. This is because current continues to flow along remaining paths in the circuit. Parallel circuits are useful if you want components to continue to work, even if one component has failed. This is why our homes are wired up with parallel circuits. Switches Switches can be added to a parallel circuit to turn components on and off. The position of switches in parallel circuit is important. If the switch is open, both lamps are off. When the switch is closed, both lamps are on. In a parallel circuit, if the switch is open, both lamps are off but when the switch is closed, both lamps are on Both switches are open and both lamps are off. The top switch is closed, and the top lamp is on. The bottom switch is open, and the lamp is off. The top switch is open, and the top lamp is off. The bottom switch is closed, and the bottom lamp is on. Both switches are closed and both lamps are on. Current and resistance in parallel circuits The current can have different values in different parts of a parallel circuit. This is because there are multiple paths for current to flow. The current is shared between the different branches of the circuit. When current reaches a junction in the circuit, it splits up and some current flows along each route. When two branches of a circuit meet, the current combines again. The total current flowing through the cell can be found by adding the individual currents flowing through each branch. The current through the cell is more than the current through each lamp in parallel. Unlike a series circuit, adding more components to a parallel circuit decreases the total of the circuit. Connecting more components into the circuit in parallel causes more current to flow through the cell, not less. Identical lamps can be added in parallel to a circuit. As more bulbs are added, the brightness of each bulb stays the same. Identical lamps have the same resistance. Each lamp in parallel has the same current passing through it. Each lamp glows with the same brightness. If the components in a parallel circuit have different resistances, a different amount of current will flow through each branch (in that loop) and the total current supplied by the battery. The greater the resistance of the component, the less current will flow through it. The current is still shared between the branches, and it still adds where the branches meet. It does not affect the current in the other loop. Since there are different loops, the current will split as it leaves the cell and pass through one or other of the loops. If one loop has less resistance than the other, there will be more current in the loop with the lower resistance. An ammeter placed in different parts of the circuit will show how the current splits: I1=I2+I4=I3 current (I) is measured in amps (A) Example: This parallel circuit contains a resistor and a lamp. A current of 5 A flows through the cell. The current splits at the junction. 3 A flows through the resistor and 2 A flows through the bulb. The total current into a junction equals the total current out of a junction. 5 A = 3 A + 2 A. The total current into a junction equals the total current out of a junction More current flows through paths with lower resistance. More current flows through the resistor, so it must have a lower resistance than the lamp. Potential difference in parallel circuits In a parallel circuit, the potential difference across each branch of the circuit is the same as the potential difference produced by the cell or battery. The potential difference is not shared between the components (like in a series circuit). Since energy has to be conserved, the energy transferred around the circuit by the electrons is the same whichever path the electrons follow. Since potential difference is used to measure changes in energy, the potential difference supplied is equal to the potential differences across each of the parallel components: Vs=V1=V2 potential difference (V) is measured in volts (V) If the resistance of any component in a parallel circuit change, this will have no effect on the potential difference across any of the components. If a second lamp is added in parallel, it also has the same potential difference across it is - the full potential difference produced by the cell. This means the same current flows through each lamp, and they both glow just as brightly. If more lamps are added to a parallel circuit, all the lamps continue to glow brightly because the potential difference is the same across all branches of a parallel circuit. All the lamps in these circuits will glow with the same brightness.