Physics 122B Electricity and Magnetism - PowerPoint

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					         Physics 122B
  Electricity and Magnetism
Lecture 16 (Knight: 31.9,10 & 32.1)
 Grounding, RC Circuits, Magnetism
            May 7, 2007




           Martin Savage
    Lecture 17 Announcements
 Lecture HW Assignment #5 has been
posted on Tycho and is due at 10 PM on
Wednesday.
 Check Tycho for your exam scores. If
there are missing parts, you may not have
put your name on your paper. See Helen
Gribble, C136 PAB, to fix such problems.


12/15/2011     Physics 122B - Lecture 17    2
            Example:
 Analyzing a Complex Circuit (2)




12/15/2011   Physics 122B - Lecture 17   3
      Maximum Power Transfer
Question: For a battery with EMF E and
internal resistance r, what value should an                         I
adjustable external load resistance R have
to make the power dissipated in R as large
as possible?
                                                            r
    E                          E 
                                   2
                                         E 2R
I               PR  I 2 R                                                   R
   rR                             R
                              rR    r  R
                                               2

                                                                E
dPR    E     2
                    E R   2
                                   rR
              2           E 2          0
dR  r  R  2
                  r  R
                          3
                                 r  R
                                        3




       PR is a maximum when r-R = 0 or r=R. In other words, energy
 can be drawn from the battery at the greatest rate when the external
 load resistance matches the internal resistance of the battery. This is
 called load matching. It is very important in transferring energy and
 signals with minimum loss. But note that only ½ of the energy gets to R.
12/15/2011                      Physics 122B - Lecture 17                   4
              Grounding and GFI
   Modern power wiring includes a “ground” line, the
round 3rd wire of an electrical plug. The ground point
defines a point of zero potential, which is normally
connected directly to the Earth (Vearth=0). The
operation of any circuit depends only on potential
differences, so it should not be affected by the
presence or absence of a ground connection.
    Because the ground connection is connected at
only one point, no current should flow through the
ground connection. However, if some other part of a
circuit is accidentally grounded, current is likely to
flow through the ground line.
   GFI (ground fault interruption) circuits, widely
used, e.g., in bathroom wiring, detect current flow in
the ground line and interrupt power automatically
when it occurs. This has prevented many accidental
electrocutions.

12/15/2011                  Physics 122B - Lecture 17    5
              Light Fixture




             V=0




12/15/2011         Physics 122B - Lecture 17   6
                  Example:
              A Grounded Circuit
  The circuit shown is grounded at
the junction between the two
resistors rather than at the bottom.
   Find the potential at each corner
of the circuit.

   E   10 V
 I             0.5 A
   R 8   12 

 V1  (8 )(0.5 A)  4 V

 V2  (12 )(0.5 A)  6 V


12/15/2011                Physics 122B - Lecture 17   7
                  RC Circuits




               I = - dQ/dt
                                                        Qf                t
                                                              dQ     1
                                                                       dt
           Q      Q    dQ               dQ     1                 
VC  VR   IR   R    0                   dt
           C      C    dt               Q     RC         Qi
                                                              Q     RC 0
   Qf      t       Qf        t                      Q f  Qi et / RC
 ln                  exp  
    Qi    RC       Qi        RC 
                                 
                                                    Exponential decay!
 12/15/2011             Physics 122B - Lecture 17                             8
             RC Exponential Decay
               t / RC           t / 
 Q(t )  Q0e              Q0e
                                                                                     t
                                                       dQ(t ) Q0                
                                              I (t )                       e      RC
                                                           dt          RC
 Define RC time constant:   RC
                                                      I 0 e  t / RC  I 0 e  t /
   1/ e  1/ 2.71828  0.367879
                                                           I0 Q0/RC




12/15/2011                 Physics 122B - Lecture 17                                     9
               Charging Capacitors:
                 Early and Late
    Initially, when a switch closes there is a potential difference of 0 V
across an uncharged capacitor. After a long time, the capacitor reaches
its maximum charge and there is no current flow through the capacitor.
Therefore, at t=0 the capacitor behaves like a short circuit (R=0), and at
t=∞ the capacitor behaves like at open circuit (R=∞).

   Example:
                                                               100 V       100 V



                                12.5 A

                                                                            100 V
                                            2.5 A   10 A        0 V


         Circuit                     at t=0                            at t=∞
                          Calculate initial currents.      Calculate final potentials.
                           IB = 100 V/8  = 12.5 A
12/15/2011                  Physics 122B - Lecture 17                               10
                Example: Exponential
                Decay in a RC Circuit
   The switch has been in position
``a’’ for a long time. It is changed to
position ``b’’ at t=0.
   What are the charge is the
capacitor and the current through the
resistor at t=5.0 ms?

  RC  (10 )(1.0 10-6 F)  10 ms

Q0  CVC  (1.0 10-6 F)(9.0 V)  9.0 10-6 C

Q(5 ms)  Q0et / RC  (9.0 10-6 C)exp(.5)  5.5 mC

     Q0 (9.0 10-6 C)
I0                   0.90 A           I (5 ms)  I0et / RC  (0.90 A)exp(.5)  0.55 A
     RC    (10 ms)
  12/15/2011                     Physics 122B - Lecture 17                           11
             Charging a Capacitor
                                     dQ 1
    Using the Loop Law: E  R           Q0
                                     dt C
                           t                    t
                                   dQ     b  RC
    Try: Q  a  be       RC
                               , so        e
                                    dt    RC

             t        t
        b  RC a b  RC
    E  e       e     a EC
        C       C C

                    dQ E    b
    At t  0, I            b  E C
                    dt R   RC

                           
                              t
                                             
                                                 t
                                                   
   Therefore, Q  E C 1  e RC   Qmax 1  e RC 
                                                

12/15/2011                           Physics 122B - Lecture 17   12
                                Question




             The time constant for the discharge of the capacitor is:



  (a) 5 s;     (b) 4 s;   (c) 2 s;   (d) 1 s; (e) the capacitor does not discharge
                                                  because the resistors cancel.


12/15/2011                       Physics 122B - Lecture 17                     13
             Plumber’s RC Analogy*
                                                               Valve   Constriction


                                                         P1                       P2




                                                        Pump        Rubber
                                                                   Diaphragm

The “plumber’s analogy” of an RC circuit is a                     P3
pump (=battery) pumping water in a closed
loop of pipe that includes a valve (=switch), a         Pump = Battery
constriction (=resistor), and a rubber                  Valve = Switch
diaphragm. When the valve starts the flow,              Constriction = Resistor
                                                        Capacitor= Rubber Diaphragm
the diaphragm stretches until the pressure
                                                        Pressure = Potential
difference across the pump (P1-P3) equals               Water Flow = Current
that across the diaphragm (P2-P3).
12/15/2011                  Physics 122B - Lecture 17                            14
       Chapter 31 Summary (1)




12/15/2011    Physics 122B - Lecture 17   15
       Chapter 31 Summary (2)




12/15/2011    Physics 122B - Lecture 17   16
       Chapter 31 Summary (3)




12/15/2011    Physics 122B - Lecture 17   17
    Experiments with Magnetism:
           Experiment 1

   Tape a bar magnet to a cork
and allow it to float in a dish of
water.

   The magnet turns and aligns
itself with the north-south
direction.

   The end of the magnet that
points north is called the
magnet’s north-seeking pole, or
simply its north pole. The
other end is the south pole.



12/15/2011                    Physics 122B - Lecture 17   18
    Experiments with Magnetism:
           Experiment 2




    Bring the north poles of two bar magnets near to each other. Then
 bring the north pole of one bar magnet near the south pole of another
 bar magnet.

    When the two north poles are brought near, a repulsive force
 between them is observed. When the a north and a south pole are
 brought near, an attractive force between them is observed.


12/15/2011                Physics 122B - Lecture 17                      19
    Experiments with Magnetism:
           Experiment 3




     Bring the north pole of a bar magnet near a compass needle.

    When the north pole is brought near, the north-seeking pole of the
 compass needle points away from the magnet’s north pole. Apparently
 the compass needle is itself a little bar magnet.


12/15/2011                 Physics 122B - Lecture 17                     20
    Experiments with Magnetism:
           Experiment 4




    Use a hacksaw to cut a bar magnet in half. Can you isolate the north
 pole and the south pole on separate pieces?

    No. When the bar is cut in half two new (but weaker) bar magnets
 are formed, each with a north pole and a south pole. The same result
 would be found, even if the magnet was sub-divided down to the
 microscopic level.


12/15/2011                 Physics 122B - Lecture 17                       21
    Experiments with Magnetism:
           Experiment 5
    Bring a bar magnet near an assortment of objects.

   Some of the objects, e.g. paper clips, will be attracted to
the magnet. Other objects, e.g., glass beads, aluminum foil,
copper tacks, will be unaffected. The objects that are
attracted to the magnet are equally attracted by the north
and south poles of the bar magnet




12/15/2011                 Physics 122B - Lecture 17             22
    Experiments with Magnetism:
           Experiment 6
   Bring a magnet near the
electrode of an electroscope.

   There is no observed effect,
whether the electroscope is
charged or discharged and
whether the north or the south
pole of the magnet is used.




12/15/2011                 Physics 122B - Lecture 17   23
     Conclusions from Experiments
1.    Magnetism is not the same as electricity. Magnetic poles
      are similar to charges but have important differences.
2.    Magnetism is a long range force. The compass needle
      responds to the bar magnet from some distance away.
3.    Magnets have two poles, “north” (N) and “south” (S). Like
      poles repel and opposite poles attract.
4.    Poles of a magnet can be identified with a compass. A
      north magnet pole (N) attracts the south-seeking end of
      the compass needle (which is a south pole).
5.    Some materials (e.g., iron) stick to magnets and others do
      not. The materials that are attracted are called magnetic
      materials. Magnetic materials are attracted by either
      pole of a magnet. This is similar in some ways to the
      attraction of neutral objects by an electrically charged
      rod by induced polarization.
12/15/2011             Physics 122B - Lecture 17             24
             Monopoles and Dipoles
    Every magnet that has ever
been observed is a magnetic
dipole, containing separated
north and south poles. Attempts
to isolate one pole from the
other fail.

    It is theoretically possible to have magnetic monopoles, i.e., isolated
magnetic poles with a “north” or “south” magnetic charge. Search have
been conducted, but no such object has ever been found in nature. For
the purposes of this course, we will assume that isolated magnetic
monopoles do not exist, but we will point out the places in the formalism
where they would go if they did exist.




12/15/2011                  Physics 122B - Lecture 17                         25
    Lecture 17 Announcements
 Lecture HW Assignment #5 has been
posted on Tycho and is due at 10 PM on
Wednesday.
 Check Tycho for your exam scores. If
there are missing parts, you may not have
put your name on your paper. See Helen
Gribble, C136 PAB, to fix such problems.


12/15/2011     Physics 122B - Lecture 17   26

				
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