Basic Concepts in DC Circuit PDF

Basic concepts in DC circuit Chapter (1) Basic concepts in DC circuit 1  Basic concepts in DC circuit Alessandro Antonio Volta (1745–1827) An Italian physicist invented the electric battery which provided the first...

Basic concepts in DC circuit Chapter (1) Basic concepts in DC circuit 1  Basic concepts in DC circuit Alessandro Antonio Volta (1745–1827) An Italian physicist invented the electric battery which provided the first continuous flow of electricity and the capacitor. Born into a noble family in Como, Italy, Volta was performing electrical experiments at age 18. His invention of the battery in 1796 revolutionized the use of electricity. The publication of his work in 1800 marked the beginning of electric circuit theory. Volta received many honors during his lifetime. The unit of voltage or potential difference, the volt, was named in his honor. Andre-Marie Ampere (1775–1836) A French mathematician and physicist laid the foundation of electrodynamics. He defined the electric current and developed a way to measure it in the 1820s. Born in Lyons, France. Ampere at age 12 mastered Latin in a few weeks, as he was intensely interested in mathematics and many of the best mathematical works were in Latin. He was a brilliant scientist and a prolific writer. He formulated the laws of electromagnetics. He invented the electromagnet and the ammeter. The unit of electric current, the ampere, was named after him. Introduction In electrical engineering, we are often interested in communicating or transferring energy from one point to another. To do this requires an interconnection of electrical devices. 2  Basic concepts in DC circuit Such interconnection is referred to as an electric circuit, and each component of the circuit is known as an element. Simple electrical circuit consists of three basic components: a battery, a lamp, and connecting wires. Figure 1.1 A simple electric circuit. The units of systems In this system, there are six principal units from which the units of all other physical quantities can be derived. Table 1.1 shows the six units, their symbols, and the physical quantities they represent. The SI units are used throughout this text. One great advantage of the SI unit is that it uses prefixes based on the power of 10 to relate larger and smaller units to the basic unit. 3  Basic concepts in DC circuit Table 1.2 shows the SI prefixes and their symbols. For example, the following are expressions of the same distance in meters (m): 600,000,000 mm 600,000 m 600 km. 4  Basic concepts in DC circuit Charge and Current Electrons have a negative charge (-) and equal in magnitude to 1.602×10−19 C. Protons have a positive charge (+). Neutrons are neutral. The negative charge of the electrons is balanced by the positive charge of the protons. Figure 1.2 Atom Figure 1.3 Electric current due to flow of electronic charge in a conductor. Electric current is the time rate of change of charge, measured in amperes (A). Mathematically, the relationship between current i, charge q, and time t is where current is measured in amperes (A), and 1 ampere = 1 coulomb / second 5  Basic concepts in DC circuit If the current does not change with time, but remains constant, we call it a direct current (dc). A direct current (dc) is a current that remains constant with time. By convention the symbol I is used to represent such a constant current. A time-varying current is represented by the symbol i. A common form of time-varying current is the sinusoidal current or alternating current (ac). An alternating current (ac) is a current that varies sinusoidally with time. Such current is used in your household, to run the air conditioner, refrigerator, washing machine, and other electric appliances. Figure 1.4 shows direct current and alternating current; these are the two most common types of current. Figure 1.4 Two common types of current: (a) direct current (dc), (b) alternating current (ac). Voltage As explained briefly in the previous section, to move the electron in a conductor in a particular direction requires some work or energy transfer. 6  Basic concepts in DC circuit This work is performed by an external electromotive force (emf), typically represented by the battery in Fig. 1.3. This emf is also known as voltage or potential difference. The voltage Vab between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically, where w is energy in joules (J) and q is charge in coulombs (C). The voltage Vab or simply v is measured in volts (V). It is evident that 1 volt = 1 joule/coulomb = 1 newton meter/coulomb Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V). Figure 1.6 shows the voltage across an element (represented by a rectangular block) connected to points a and b. The plus (+) and minus (−) signs are used to define reference direction or voltage polarity. The v ab can be interpreted in two ways: (1) point a is at a potential of vab volts higher than point b, or (2) the potential at point a with respect to point b is vab. It follows logically that in general Vab = −Vba Figure 1.5 Polarity of voltage Vab. 7  Basic concepts in DC circuit Like electric current, a constant voltage is called a dc voltage and is represented by V, whereas a sinusoidally time-varying voltage is called an ac voltage and is represented by v. A dc voltage is commonly produced by a battery; ac voltage is produced by an electric generator. Power And Energy Although current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves. For practical purposes, we need to know how much power an electric device can handle. We all know from experience that a 100-watt bulb gives more light than a 60-watt bulb. We also know that when we pay our bills to the electric utility companies, we are paying for the electric energy consumed over a certain period of time. Thus power and energy calculations are important in circuit analysis. Power is the time rate of expending or absorbing energy, measured in watts (W). We write this relationship as: where p is power in watts (W), w is energy in joules (J), and t is time in seconds (s). From above, it follows that Thus, the power absorbed or supplied by an element is the product of the voltage across the element and the current through it. If the power has a + sign, power is being delivered to or absorbed by the element. If, on the other hand, the power has a − sign, power is being supplied by the element. But how do we know when the power has a negative or a positive sign? 8  Basic concepts in DC circuit Current direction and voltage polarity play a major role in determining the sign of power. It is therefore important that we pay attention to the relationship between current i and voltage v in Figure. 1.6(a). The voltage polarity and current direction must conform with those shown in Figure. 1.6(a) in order for the power to have a positive sign. This is known as the passive sign convention. By the passive sign convention, current enters through the positive polarity of the voltage. In this case, p = +vi or vi > 0 implies that the element is absorbing power. Figure 1.6 Reference polarities for power using the passive sign convention: (a) absorbing power, (b) supplying power. However, if p = −vi or vi < 0, as in Figure. 1.6(b), the element is releasing or supplying power. Passive sign convention is satisfied when the current enters through the positive terminal of an element and p = +vi. If the current enters through the negative terminal, p = −vi. Unless otherwise stated, we will follow the passive sign convention throughout this text. For example, the element in both circuits of Figure. 1.7 has an absorbing power of +12 W because a positive current enters the positive terminal in both cases. 9  Basic concepts in DC circuit Figure 1.7 Two cases of an element with an absorbing power of 12 W: (a) p = 4 × 3 = 12 W, (b) p = 4 × 3 = 12 W. In Figure. 1.8, however, the element is supplying power of −12W because a positive current enters the negative terminal. Of course, an absorbing power of +12 W is equivalent to a supplying power of −12 W. In general, Power absorbed = −Power supplied In fact, the law of conservation of energy must be obeyed in any electric circuit. For this reason, the algebraic sum of power in a circuit, at any instant of time, must be zero: Figure 1.8 Two cases of an element with a supplying power of 12 W: (a) p = 4 × (-3) = -12 W, (b) p = 4 × (-3) = -12 W. 10  Basic concepts in DC circuit Circuit Elements An electric circuit is simply an interconnection of the elements. Circuit analysis is the process of determining voltages across (or the currents through) the elements of the circuit. There are two types of elements found in electric circuits: passive elements and active elements. An active element is capable of generating energy while a passive element is not. Examples of passive elements are resistors, capacitors, and inductors. Typical active elements include generators, batteries, and operational amplifiers. Our aim in this section is to gain familiarity with some important active elements. The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them. There are two kinds of sources: independent and dependent sources. An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit variables. Physical sources such as batteries and generators may be regarded as approximations to ideal voltage sources. Figure 1.9 shows the symbols for independent voltage sources. Notice that both symbols in Figure. 1.9(a) and (b) can be used to represent a dc voltage source, but only the symbol in Figure. 1.9(a) can be used for a time-varying voltage source. 11  Basic concepts in DC circuit Figure 1.9 Symbols for independent voltage sources: (a) used for constant or time- varying voltage, (b) used for constant voltage (dc). The symbol for an independent current source is displayed in Fig. 1.10, where the arrow indicates the direction of current i. Figure 1.10 Symbol for independent current source. An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current. Dependent sources are usually designated by diamond-shaped symbols, as shown in Fig. 1.11. Since the control of the dependent source is achieved by a voltage or current of some other element in the circuit, and the source can be voltage or current, it follows that there are four possible types of dependent sources, namely: 1. A voltage-controlled voltage source (VCVS). 2. A current-controlled voltage source (CCVS). 3. A voltage-controlled current source (VCCS). 4. A current-controlled current source (CCCS). 12  Basic concepts in DC circuit Figure 1.11 Symbols for: (a) dependent voltage source, (b) dependent current source. Dependent sources are useful in modeling elements such as transistors, operational amplifiers and integrated circuits. An example of a current controlled voltage source is shown on the right-hand side of Fig. 1.12, where the voltage 10i of the voltage source depends on the current i through element C. Students might be surprised that the value of the dependent voltage source is 10i V (and not 10i A) because it is a voltage source. The key idea to keep in mind is that a voltage source comes with polarities (+ −) in its symbol, while a current source comes with an arrow, irrespective of what it depends on. Figure 1.12 The source on the right-hand side is a current-controlled voltage source. 13  Basic concepts in DC circuit It should be noted that an ideal voltage source (dependent or independent) will produce any current required to ensure that the terminal voltage is as stated, whereas an ideal current source will produce the necessary voltage to ensure the stated current flow. Thus, an ideal source could in theory supply an infinite amount of energy. It should also be noted that not only do sources supply power to a circuit, but they can also absorb power from a circuit too. For a voltage source, we know the voltage but not the current supplied or drawn by it. By the same token, we know the current supplied by a current source but not the voltage across it. Example (1) Calculate the power supplied or absorbed by each element in the following figure. Solution: For p1, the 5-A current is out of the positive terminal (or into the negative terminal); hence, p1 = 20(−5) = −100 W Supplied power For p2 and p3, the current flows into the positive terminal of the element in each case. p2 = 12(5) = 60 W Absorbed power p3 = 8(6) = 48 W Absorbed power 14  Basic concepts in DC circuit For p4, we should note that the voltage is 8V (positive at the top), the same as the voltage for p3, since both the passive element and the dependent source are connected to the same terminals. (Remember that voltage is always measured across an element in a circuit.) Since the current flows out of the positive terminal, p4 = 8(−0.2I) = 8(−0.2 × 5) = −8 W Supplied power We should observe that the 20-V independent voltage source and 0.2I dependent current source are supplying power to the rest of the network, while the two passive elements are absorbing power. Also, p1 + p2 + p3 + p4 = −100 + 60 + 48 − 8 = 0 15  Basic concepts in DC circuit Quiz 1 One millivolt is one millionth of a volt. (a) True (b) False 2 A 4A current charging a dielectric material will accumulate a charge of 24 C after 6 s. (a) True (b) False 3 A charge of 2 C flowing past a given point each second is a current of 2 A. (a)True (b) False 4 The prefix micro stands for 10-3: (a)True (b) False 5 The voltage 2,000,000 V can be expressed in powers of 10 as 2 MV: (a)True (b) False 6 The unit of current is: (a) Coulomb (b) Ampere (c) Volt (d) Joule 7 Voltage is measured in: (a) Watts (b) Amperes (c) Volts (d) Joules/second 8 The voltage across a 1.1 kW toaster that produces a current of 10 A is: (a) 11 kV (b) 1100 V (c) 110 V (d) 11 V 9 Which of these is not an electrical quantity? (a) charge (b) time (c) voltage (d) current (e) power 10 The dependent source in Fig. is: (a) voltage-controlled current source (b) voltage-controlled voltage source (c) current-controlled voltage source (d) current-controlled current source 16  Basic concepts in DC circuit 17  Basic concepts in DC circuit Problems Problem (1) The Figure below shows a circuit with five elements. If p1 = −205 W, p2 = 60 W, p4 = 45 W, p5 = 30 W, calculate the power p3 received or delivered by element 3. Problem (2) A 1.5kW electric heater is connected to a 120V source. i. How much current does the heater draw? Problem (3) Find the power absorbed by each of the elements in the Fig. below. Problem (4) Determine I o in the circuit of the Fig. below. 18  Basic concepts in DC circuit Problem (5) Find V o in the circuit of the Fig. below. 19