2. Basic Components and Electrical Circuits


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1 1 2. Basic Components and Electrical Circuits 2.1 Units and Scales The International System of Units (SI) defines 6 principal units from which the units of all other physical quantities can be derived Table 2.1 SI base units Basic Quantity Unit Symbol Length Mass Time Electric current Thermodynamic temperature Luminous intensity meter kilogram second ampere kelvin candela m kg s A K cd The SI unit of work or energy is the joule (J), which equals to a kg m 2 s 2 in SI base units The SI unit of power is equivalent to one joule per second
2 2 The SI unit uses prefixes based on the power of 10 to relate larger and smaller units to the basic unit Table 2.2 SI prefixes Basic Quantity Name Symbol tera giga mega kilo centi milli micro nano pico T G M k c m n p
3 3 2.2 Circuit Variables Charge Electric charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C) The charge of an electron is X C The coulomb is a large unit for charges such that in 1 C of charge, there are 1/(1.602 X )=6.24 X electrons The realistic or laboratory values of charges are on the order pc, nc, and μc Current Electric current is a flow of electric charge measured in ampere (A) note that 1 ampere (A) is equal to 1 coulombs per second (C/s)
4 4 The total charge transferred between time t 0 and t can be expressed as There are several different types of current Direct current (dc) Sinusoidal current (ac) Exponential current Damped sinusoidal currents Representation of current in circuit analysis
5 5 Practice In the wire of shown figure, electrons are moving left to right to create a current of 1 ma. Determine and Ans: the current is in the opposite direction to flow of electrons Voltage Voltage or potential difference measured in volts (V) is the energy required to move a unit of charge through an element note that 1 volt (V) is equal to 1 joule per coulombs (J/C)
6 6 Representation of voltage in circuit analysis The plus (+) and minus () signs at the points a and b are used to define a reference direction (the voltage polarity) Similar to the electric current, a constant voltage is called a dc voltage, whereas a sinusoidal voltage (timevarying) is called an ac voltage For practical purposes, the power and energy are important measures in circuit analysis
7 Power Measured in watts (W) to indicate the average absorbing energy by a circuit element The sign of power + sign: the power is absorbed by the element (resistor)  sign: the power is supplied by the element (?) Since the energy can neither be created or dissipated (only transferred), the algebraic sum of powers in a circuit, at any instant of time, must be zero
8 8 Determine p 1 Ans: Energy The energy absorbed or supplied by an element from time 0 to t is Electricity bills:: The electric power utility companies measure energy in kilowatthours (kwh), where 1 kwh = 3600 kj
9 9 2.3 Voltage and Current Sources There are two types of circuit elements: Active elements (supplying energies), e.g., electric generator, batteries Passive elements (absorbing energy), e.g., resistors, capacitors, and inductors The passive elements can be classified according to the relationship of the current through it to the voltage Resistor, Capacitor, Inductor, Voltage and current sources: Voltage sources provides the circuit with a specified voltage Current source provides the circuit with a specified current
10 10 Independent voltage source The source is characterized by a terminal voltage which is completely independent of the current through it dc voltage source ac voltage source Independent current source The current through the element is completely independent of the voltage across it dc current source ac current source
11 11 Dependent sources The value of dependent sources depends on a voltage or currents of some other elements There are 4 different types of dependent sources currentcontrolled current source voltagecontrolled current source voltagecontrolled voltage source currentcontrolled voltage source Find v L Ans:
12 12 Dependent sources The value of dependent sources depends on a voltage or currents of some other elements There are 4 different types of dependent sources currentcontrolled current source voltagecontrolled current source voltagecontrolled voltage source currentcontrolled voltage source Find the power absorbed by each element in the circuit Ans:
13 Ohm's Law Ohm's law states the voltage across conducting materials is directly proportional to the current flowing through the material, or where R is the resistance slope=r (V/A) The unit of the resistance is Ohm (Ω) The Resistor has a linear relation between the applied voltage and the current The current goes from a higher potential to a lower potential The power absorbed by the resistor can be expressed as The resistor is a passive element that cannot deliver or store energy Find i and R, if v=10 V and R is absorbing 0.1 W Ans:
14 14 The resistance of any cylindrical object is given as l Material with resistivity ρ A For a linear resistor, the ratio of the current to the voltage is called the conductance The SI unit of the electrical conductance G is siemens (S) Homework Assignment 1 P2.11, P2.12, P2.15, P2.17, P2.20, P2.22, P2.23, P2.26, P2.31, P2.32, P2.33, and P2.35
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