Let s go to something more concrete

Transcription

1 Let s go to something more concrete Let me define an electric current Whenever charges of like sign are moving, an electric current exists Suppose I have a surface A with charges (assume + because of Franklin s convention) moving through it I define the current I as the rate at which charge flows through this surface u I = DQ/Dt Let s think about units: [I] = [Q]/[t] [I] = C/s = A(mps) 1 Amp = 1 C/s How many electrons/sec in a current Fig. 17.1, p.531 of 1 A?

2 Direction of current We define the direction of electrical current as being the direction that positive charges would flow Even though we know that in the cases we will be dealing with, it s negatively charged conduction electrons that are moving Blame Benjamin Franklin

3 Consider charges moving through 4 regions of space Which of the figures has the largest current? Which has the smallest? largest smallest Note that for this exercise, we are using a situation where both + and - charges can move (for example, through free space). Fig. 17.2, p.532

4 Current and drift speed Suppose I have a conductor with electrical charges q moving at a speed v d (drift speed) Consider the volume element ADx u if the density of mobile charge carriers is n, then number of mobile charge carriers in volume is nadx u DQ = (nadx)q If charges move with constant average speed v d, then in time Dt, they move u Dx = v d Dt amount of mobile charge DQ is then u DQ = (nav d Dt)q Current I is u I =DQ/Dt = nqv d A What s a typical value for v d? Fig. 17.3, p.532

5 So what, are the electrons lazy? No, they re actually moving very fast (~1E5 m/s), but in random directions because they keep bumping into atoms and changing directions And there s really no place in particular that they want to go, unless there s an electric field in the conductor But I thought we couldn t have an electric field inside a conductor u we can t, for static conditions, but these aren t static conditions If v d is so small, then why did the light bulbs light up immediately? F = -e E let s do marbles and nails Fig. 17.4, p.533

6 How do I create an electric field in a conductor? By creating an electric potential difference, for example by using a battery u represent a battery by + - from Cartoon History of Physics the + terminal is at a higher potential then the negative terminal each cell can typically create a potential difference of V

7 Electrical Circuit Diagram I draw lines to connect the battery and the light bulb in a complete circuit. I e- I have also inserted 2 devices into the circuit: an ammeter and a voltmeter. Fig. 17.5, p.535

8 Which of these circuits will light the bulb? Nope Nope Yep Yep Fig. 17.6, p.536

9 Resistance and Ohm s Law Suppose I apply a potential difference across a conductor. The current through the conductor is found to be proportional to the voltage difference across it. I a DV Define resistance R = DV/I DV = V a -V b [R] = [DV]/[I] [R] = V/A [R] = W (ohms) - + DV = V a -V b = E l

10 Ohm s Law For many materials the resistance remains constant as the voltage is changed. but not for all DV = IR ->Ohm s Law semi-conductor diode Fig. 17.8, p.537

11 Resistance and resistivity Resistance of a conductor, say, is proportional to the length of the conductor and inversely proportional to the cross-sectional area of the conductor u R a l /A But it also depends on some intrinsic property of the conductor; how easy it is for the conduction electrons to move through the conductor u let s call it the resistivity r u R = r l /A from Cartoon History of Physics

12 Resistivities Wide range of resistivities for different materials Low resistivities correspond to good conductors Large resistivities correspond to good insulators

13 Examples of resistors Most of resistance in a circuit is not in the conducting wires but in devices inserted in the circuit called resistors. Fig. 17.p537, p.537

14 Electrical circuits I ll represent the electrical resistance of an element in a circuit by using this jagged line symbol u the lines connecting the circuit components have no resistance; all resistance is summarized in R Note this new symbol here denoting electrical ground

15 Temperature Variation The resistivity of a material is not constant but varies as a function of temperature (usually increasing) u r = r o [1+a(T-T o )] u a is the temperature coefficient Fig. 17.T1, p.538