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Electric Current Current Rate at which charge passes a given point in a circuit in one second Flow of coulombs Ampere (A) is unit of current (I) I = Δq t Ammeter measures current Electric Circuit is a closed path along which charged particles move Current Calculation A total of 20.0C of charge pass a given point in a conductor in 4.0 seconds. Determine the current in the conductor. I = Δq = 20.0C = 5A t 4.0s Conditions Necessary For An Electric Circuit A potential difference between two points. A voltage source for energy supplied by a battery (cell), power company, or transformer. A battery supplies the force or push on electrons to move Voltmeter measures potential energy. A closed path Conductivity In Solids Conductivity – availability of charges that are relatively free to move under the influence of an electric field Conductors – lots of free electrons, metals Insulators – tightly held electrons, nonmetals Ohms Law Opposition that a device or conductor offers to the flow of electric current R=V R = resistance I V = volts I = current Ohm(Ω) is the unit of Resistance 1Ω = volt amp Example: A current of 0.10 ampere flowing through a lamp connected to 12.0 volt source. What is the resistance of the lamp? V = 12.0V R = V = 12.0V = 120Ω I = 0.10A I 0.10A Factors That Affect The Resistance Of A Conductor Resistivity Temperature affects o solids, temperature increases R increases o Liquids, temperature increases R decreases Length and cross-section of wire R = рL A р = resistivity of material A = cross-sectional area R = resistance Example: A piece of wire has a resistance of 8 ohms. What is the resistance of a second piece of wire of the same composition, same diameter and at the same temperature, but with one half the length of the first wire? 4 Ohms Example: A 5.00M long tin wire has a cross-sectional area of 2.00 x 10^-6m² and a 0.35 ohm resistance. Determine the resistivity of tin. p = AR = (2.00 x 10^-6m²)(0.35Ω) = 1.4 x 10^-7Ω·m L 5.00m Resistor – limits current flow or provides a potential (voltage) drop Electric Circuits Electric Circuit Symbols Switch A Ammeter Cell Battery V Voltmeter Resistor Variable Resistor Series Circuit Only one current path Current is the same everywhere in the circuit IT = I1 = I 2 = I3 The sum of all the potential drops (individual voltage readings) equals the total voltage in the circuit V T = V 1 + V 2 + V3 The sum of individual resistor readings equals the total resistance of the circuit RT = R1 + R2 + R3 RT = equivalent(eq) R Conservation of Charge VT out = VT in IT out = IT in 8v 2A R1 4Ω + 36V 12v 16v R2 6Ω R3 8Ω 2A Voltmeters are placed across components of a circuit or “in parallel” Ammeters are placed in the circuit or “in series” 2A V1 V2 R1 4Ω R2 6Ω + V3 R3 8Ω 2A 36V Find the total resistance (equivalent resistance): RT = R1 + R2 + R3 = 4Ω + 6Ω + 8Ω = 18Ω Find the total current: IT = VT = 36V = 2A RT 18Ω Find the current in each circuit: IT = I1 = I2 = I3 2A! Find the voltage drop across each resistor: V1 = I1R1 = (2A)(4Ω) = 8V V2 = I2R2 = (2A)(6Ω) = 12V V3 = I3R3 = (2A)(8Ω) = 16V Find the total power used by the circuit: PT = VTIT = (36V)(2A) = 72W Find the power used by the 6Ω resistor: P2 = V2I2 = (6Ω)(2A) = 12W Find the amount of heat given off by the 6Ω resistor in 30 seconds: W = Pt = (12W)(30s) = 360J Same Circuit, Different Drawing 12V R2 6Ω R14Ω 8V 16V 8Ω R3 36V 2A 2A Parallel Circuit More than one current path The total current is the sum of the branch currents IT = I1 + I 2 + I3 The total voltage is the same as the voltage reading across each resistor V T = V 1 = V 2 = V3 The sum of the reciprocals of the branch resistors is equal to the total resistance (equivalent resistance) 1 = 1 + 1+ 1 RT R1 R2 R3 12V V 3A R1 4Ω 12V 2A R2 6Ω 12V 1A R3 12Ω 6A 6A + 12V - 12V 3A R1 4Ω 12V 2A R2 6Ω 12V 1A R3 12Ω 6A 6A + _ 12V Find the total resistance (equivalent resistance) 1 = 1 + 1 + 1 = 1 + 1 + 1 RT R1 R2 R3 4Ω 6Ω 12Ω 1 = .25Ω + .17Ω + .08Ω RT 1 = .5Ω RT RT = 2Ω RT is smaller than any one resistor in the circuit! Find the voltage drop across each resistor VT = V1 = V2 = V3 VT = 12V Find the total current in the circuit IT = VT = 12V = 6A RT 6Ω Find the current in each of the resistors I1 = V1 = 12V = 3A R1 4Ω I2 = V2 = 12V = 2A R2 6Ω I3 = V3 = 12V = 1A R3 12Ω IT = 3A + 2A + 1A = 6A Find the total power used by the circuit PT = VTIT = (12V)(6A) = 72W Find the power used by R2 P2 = V2I2 = (12V)(2A) = 24W Adding more branches with more resistors increases the total current in the circuit