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chapter17_updated

# chapter17_updated - Current and Resistance When charges...

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1/30/2009 1 Current and Resistance When charges move , they produce electrical current How do we define/measure/calculate the current? The amount of charges that are moving How fast they move

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1/30/2009 2 The (average) current is the rate at which the charge flows through a surface Look at the charges flowing perpendicularly through a surface of area A The SI unit of current is Ampere (Amp, A); 1 A = 1 C/s t Q I av We have about 200 students in this class Suppose each students carries 1 C charge After the class, it takes 100 seconds for all students to exit the classroom What is the average current flowing out of the door during this 100 sec interval? t Q I av A 2 100 200
1/30/2009 3 The current passing through the filament of a light bulb is 2 A. What is the amount of charge that passes in 4 sec? (1) 0.5 C (2) 2 C (3) 4 C (4) 8 C 1 A = 1 C/s t Q I av The direction of the current is defined as the direction positive charge would flow (for historical reasons) In common conductors , such as copper, aluminum, etc, the current is due to the motion of the negatively charged electrons When electrons move, they produce a current in the opposite direction What happens if both positive and negative charges move in a device? - - - - I + + + + I

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1/30/2009 4 The magnitude of the current (arbitrary units) (a) 3 + 2=5 (b) 3 (c) 2+2=4 (d) 2 Note that in this problem, the negative and the positive charges move in opposite directions , therefore their currents add up. If they move in the same direction , the currents cancel (partially or completely). Which one on the right has the same current as that in the above? (Assume the speeds of all charges are the same) (1) A (2) B (3) C + + + + + + + + + + + - + + + + - - + + + + - - A B C
1/30/2009 5 When students exit the classroom, some may move faster, some may move slower, the rate of flow varies with time How do we define the current at a given time , say t ? The instantaneous current is the limit of the average current as the time interval goes to zero: If there is a steady current, the average and instantaneous currents will be the same t Q I I t av t inst 0 0 lim lim There are some 10 22 /cm 3 electrons in a typical metal (copper, aluminum, etc) Electrons in a conductor move like crazy: They frequently bump into atoms and change their direction of motion abruptly In the absence of an external electric field, the average speed of electrons, called drift speed , , is zero; therefore no net current in the absence of an external field light) of speed the 1% about ( / 10 ~ 6 s m v d v

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1/30/2009 6 When an external field is applied to a conductor, there is a non vanishing average speed (drift speed, ) of electrons The net motion of electrons is opposite the direction of the electric field The direction of electric field is the same as the direction of current Drift speed is usually much smaller than the true speed of electrons in a conductor d v I Suppose a conducting wire has a charge carrier density n, each
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