Electric Charge, Current, and Power Concepts (EELEC1 PDF)

Electric Charge – is carried by the electrons Drift Velocity of Conduction Electrons – the and proton within an atom. drift velocity of the conduction electrons is very small since the number of free electrons in a El...

Electric Charge – is carried by the electrons Drift Velocity of Conduction Electrons – the and proton within an atom. drift velocity of the conduction electrons is very small since the number of free electrons in a Electrons carry negative charge, while protons conductor is very large. carry positive charge. The SI unit of electric charge is coulomb. One electron or proton has a charge of 1.6 x 10-19 coulomb I = current flowing, in amperes (A) Note: Copper is used as a universal reference n = electron density, in electrons/m3 conductor. 1 cubic centimeters of copper has e = charge per electron (1.6 x 10-19 C) A = cross-sectional area of the conductor (m2) 8.5 x 1022 free electrons. V = drift velocity of the electrons (m/s) V=1cm3 Example: A copper wire having a cross-sectional Free Electrons – are electrons which are not area of 1 mm2 is carrying a current of 15 attached to a specific atom and its free to A. If the density of the free electrons in the wire move. It is sometime called as conduction is 1 x 1028 e/m3, what is the drift velocity of the electrons. electrons? Example: Solve the number of free electrons in a copper conductor having a diameter of 1.6 mm and a length of 10 m. Note: 1.6 mm = 0.16 cm; 10 m = 1000 cm Electromotive Force (emf or voltage) – the energy provided by a cell or battery or a generator per coulomb of charge passing Electric Current – rate of electron movement or through it. The SI unit of emf is joule per electron flow in a given material. The SI unit of coulomb or commonly called volt. current is coulomb per second or commonly called ampere. E = emf or voltage, in volts (V) W = energy, in joules (J) I = current flow, in amperes (A) Q = charge, in coulombs (C) Q = total charge moving, in coulombs (C) Example: What quantity of charge must be t = time occurrence, in seconds (s) delivered by a battery with a potential Example: If a current of 2 A flows through a difference of 100 V to do 500 J of work? point in a wire for 30 seconds, how many coulombs pass through the point in the wire? Electric Energy and Power Resistance Resistivit Length Area Electric energy is a form of energy used to run ohm ohm-m m m2 or operate various electrical devices. Standard ohm ohm-CM/ft ft CM unit of electrical energy is joule or kilojoule. The other common units are kilowatt-hour and Specific resistance or resistivity of a material is megawatt-hour. the resistance offered by 1 m length of the material having a cross-sectional area of 1 m2. Electric power is the rate of consuming the electric energy. Standard unit of electrical At 20C̊, the resistivity of annealed copper wire power is watt (bigger units are kilowatt and is, megawatt). Note: If not specified, a copper wire is assumed an annealed copper wire and at 20C̊ conditions. Circular Mil (CM) – is an old unit in specifying W = electric energy, in joules (J) the cross-section area of a wire. It is equal to the area of a circle having a diameter of 1 mil. P = electric power, in watts (W) I = current, in amperes (A) E = emf or voltage, in volts (V) t = time, in seconds (s) A = d2 Example: A radio receiver draws 0.9 A at 110 V. A = cross-section area of the wire, in cmils (CM) If the set is used 3 hours per day, how much d = diameter of the wire, in mils energy does it consume in 10 days? Note: 1 inch = 1000 mils; 1 MCM = 1000 CM Relation between a Circular Mil and a Square Mil Electric Resistance – property of a material to oppose or resist the electron flow. The SI unit is A = 1 circular mil A = 1 sq. mil ohm. Note: The resistance of a conductor varies directly as the length and inversely to the cross- sectional area. Example: A 400,000-cir-mil cable is composed of 37 strands. What is the diameter, in mils, of each strand? R = resistance of the given conductor, in ohms (Ω) ρ = resistivity of the given conductor, (Ω-m) L = length of the given conductor, in meter (m) A = cross-sectional area of the conductor, (m2) Example: What length of wire of diameter 0.315 Conductance – the reciprocal of resistance. The mm will be required to construct a coil of SI unit of conductance is siemens. The old unit resistance 10 ohms, if the specific resistance of is called mho. the wire is 49 μΩ-cm? G = conductance, in siemens (S) R = resistance, in ohms (Ω) Conductivity – the reciprocal of resistivity. The SI unit is siemens per meter. Example: A standard copper wire is 0.064 inch in diameter. What is the resistance of 1000 ft of this wire at 20C̊? σ = conductivity, siemens/meter (S/m) ρ = resistivity, ohm-meter (Ω-m) Example: Solve the length of a given wire having a diameter of 1.6 mm and a resistance of 1 ohm. Conductivity of the given wire is 5 x 10^7 Wires Undergoing Drawing Processes S/m Assuming no materials were wasted during the drawing process, the resistance of the wire varies directly as the square of the length of it varies inversely as the fourth power of its diameter. Percent Conductivity Example: A length of wire has a resistance of 5 ohms. The wire is drawn until its length As a standard, the reference conductor is the becomes doubled. What will be the new annealed copper whose resistivity is 10.37 Ω- resistance? CM per foot. Thus, 100% conductivity refers to annealed copper. Example: A length of wire has a wire diameter of 10 mm and a resistance of 2 Ω. The wire is drawn reducing its diameter to 5 mm. What will be the new resistance? Example: A given wire with a length 1000-ft and Example: A given conductor has a resistance of a cross-section diameter of 0.4 inch has a 50 ohms when its temperature is 0C̊. resistance of 0.15 ohm at 20C̊. What is its Calculate its resistance at 60C̊ if the percent conductivity? temperature coefficient of resistance of the material at 0C̊ is 0.0043. Note: 0.4 inch = 400 mils Effect of Change in Temperature to the Resistance of a Conductor The resistance of all conductors will increase as the temperature of the conductor increase. R1 = resistance at temperature t1 R2 = resistance at temperature t2 T = inferred absolute zero temperature Note: For annealed copper wire, the inferred absolute zero temperature is 234.5C̊ Let: α =____ , then α = temperature coefficient of resistance at t1 Note: For annealed copper wire, the inferred absolute zero temperature is 234.5C̊ Example: A copper winding has a resistance of 0.25 ohm at a temperature of 18C̊. Calculate the temperature in the winding when after a period of operation, the resistance increases to 0.31 ohm.