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Lecture 5 Current and Resistance Chapter 17 Outline • • • • Electric Current Ohm’s Law Resistivity Electrical Energy and Power Electric Current An electric current is a flow of like charges (positive or negative). The current is the rate at which charge flows through a conducting surface. The direction of an electric current is the direction of positive charge flow (current carriers are electrons). Q I t Unit of current is ampere (A) 1A 1C/s 1A of current is equivalent to 1C of charge passing through the crossectional area in a time interval of 1 second. Electric Current Microscopic view of electric current Representation of electric current Resistance When a potential difference (V) is applied across the end of a conductor, the current in the conductor is proportional to the applied voltage. I ~ V The proportionality constant R is called the resistance. It remains constant over a wide range of currents and voltages. V R I Ohm’s Law The relationship between the current and voltage is called Ohm’s Law after George Ohm. V = IR Unit of resistance is ohm () V is the potential drop across the resistor I is the current in the resistor Materials with a constant resistance are called ohmic, those with variable resistance are nonohmic. Using Ohm’s Law Problem: How long can a car with a 12V battery of 60 A h capacity have the lights, of total resistance of 4 , on before the battery runs down? Solution: I = V /R = 12V / 4 = 3 A Time t = 60 A h / 3 A = 20 hours Resistivity Electrons, driven by the electric force inside a conductor, collide with atoms and experience an internal friction. This is the origin of a material’s resistance. The resistance of an ohmic conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). l R= A The constant is called the resistivity of the material. =R A / l is measured in m (ohm-meters). Resistance of a Wire Problem: Calculate the resistance per unit length of an aluminum (Al) wire of radius 0.5 mm. Solution: The cross-sectional area is A = r2 A = 3.1416 (0.5 103 m)2 = 7.85 107 m2 The resistivity of Al is 2.82 10 8 m Resistance per unit length is R/l = /A 2.82 10 8 m = = 0.036 /m A 7.85 107 m2 Electrical Energy and Power The chemical energy of a battery is constantly transformed into internal energy of a conductor. Q V = I V t Power P = I V V = I R P=I2R= (V)2/R Unit of power 1W = 1V 1A Units of Power and Energy Unit of power is Watt (W). Power is energy per unit time. Thus, energy can be measured in kilowatt-hours. This is not a standard unit, because the SI unit for power is W and for time is s. 1 kWh = (103 W) (3600 s) = 3.6 106 J Summary • Electric current is a flow of charge in an electric field • Resistance of a conductor is the ratio of the potential difference across the conductor to the current • Ohm’s law states that the potential difference is directly proportional to the current • Resistivity is an intrinsic property of a conductor characterizing its ability to resist to the current