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Lecture 5 Current and Resistance Chapter 17 Outline Electric Current Ohm’s Law Resistivity Electrical Energy and Power

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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.

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Electric Current Microscopic view of electric current Representation of electric current

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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

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Ohm’s Law The relationship between the current and voltage is called Ohm’s Law after George 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. V = IRUnit of resistance is ohm ( )

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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

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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).

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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 = r 2 A = 3.1416 (0.5 10 3 m) 2 = 7.85 10 7 m 2 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 10 7 m 2

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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=I 2 R= ( V) 2 /R Unit of power 1W = 1V 1A

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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 = (10 3 W) (3600 s) = 3.6 10 6 J

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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

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