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					                                               Electric Circuits                                                        IB 12
     In the electric circuit shown below, energy is transferred from the battery to the light bulb by charges
    that move through a conducting wire because of a potential difference set up in the wire by the battery.


                                                        The circuit shown contains a typical 9-volt battery.

                                                        a) What is the emf of the circuit?


                                                        b) How much energy does one coulomb of charge carry around the circuit?


                 Schematic
                                                        c) How much energy do two coulombs of charge carry around the circuit?



                                                        d) How much energy does each coulomb of charge have at point B?


                                                        e) How much energy does each coulomb of charge have at point C?


                                                        f) What is VB?               What is VC?
        mark potentials at each spot
                                                        g) What is ΔVBC?            What is ΔVCD?                 What is ΔVDA?


                                   Electric Current

    Formula:                        Units:                          Type:
    I = Δq/Δt                  A (ampere) = C/s                     Scalar



    Unofficial definition: rate of flow of electric charge

                            Official Definition of One Ampere (1 A) of current – a fundamental unit

    One ampere is the amount of current flowing in each of two infinitely-long parallel wires of negligible cross-sectional area
   separated by a distance of one meter in a vacuum that results in a force of exactly 2 x 10 -7 N per meter of length of each wire.

         Short form – Current is defined in terms of the force per unit length between parallel current-carrying conductors.



Closed circuit: complete pathway      Open circuit: incomplete pathway for current –         Short circuit: circuit with little to no
for current                           break in circuit – infinite resistance                 resistance – extremely high current –
                                                                                             overheating
                                      sketch
                                                                                             sketch




                                                                                                                             1
                                              Resistance                                           IB 12
Resistance: ratio of potential difference applied               Formula:                   Units:              Type:
across a piece of material to the current through the
material                                                        R=V/I             ohm (Ω) = V/A                scalar




For a wire conductor:                                           Formula:

A short fat cold wire is the best conductor                     R = ρL/A

A long hot skinny wire has the most resistance


Power: energy per unit time                                                Unit: W = J/s            Type: scalar

 Mechanical Power:            Electrical Power:            Alternate Formulas:
                              P = E/t = (Δq V)/Δt          Substitute V = IR
 P = W/t = F s/t = F v
                              P=IV                         P = I (IR) = I2 R

                                                           P = (V/R)V = V2/ R




  Meters in a circuit                                           Ammeter: measures current


                                                                Placement: Must be placed in series to allow
                                                                current to flow through it

                                                                Circuit must be broken to insert ammeter


                                                                Ideal ammeter: has zero resistance so it will not
                                                                affect current flowing through it


   Schematic diagram
                                                                Voltmeter: measures potential difference


                                                                Placement: Must be placed in parallel to measure
                                                                potential difference between two points
                                                                circuit does not to be broken


                                                                Ideal voltmeter: has infinite resistance so it will not
                                                                allow any current to flow through it and disrupt circuit



                                                                                                        2
                                   Series and Parallel Circuits                                  IB 12




     Characteristic                 Series Circuit                            Parallel Circuit
   Number of pathways
                                            one                                   More than one
   for current
                               Same everywhere – same for all
   Current                                                             Current splits – shared among devices
                                         devices
   Potential Difference       Voltage shared among devices –
                                                                               Same for all devices
   (Voltage)                           voltage splits

   Overall resistance                      high                                        low


   Power                                    low                                        high

                                          VT = V1 + V2 + …                        VT = V1 = V2 = . . .
    Formulas:
                                           IT = I1 = I2 = …                        IT = I1 + I2 + . . .

                                          RT = R1 + R2 + …                     1/RT = 1/R1 + 1/R2 + . . .

                                          PT = P1 + P2 + . . .                    PT = P 1 + P2 + . . .


                 Series Circuits                                          Parallel Circuits
Voltage Ratio                                          Current Ratio




Power Ratio                                            Power Ratio




                                                                                                       3
                                                  Analyzing Circuits                                                  IB 12
                    Determine the current through and the voltage drop across each resistor in each circuit below.

1.                                                                   2.




  3.                                                                 4.




  Potential Divider: Resistors in series act as a “potential (voltage) divider.” They split the potential of the source between them.

  5. A 20Ω device requires 40 V to operate properly but no 40 V source is available. In each case below, determine
      the value of added resistor R1 that will reduce the voltage of the source to the necessary 40V for device R 2.




           (A)                                (B)                                  (C)                                (D)

6. A mini light bulb is rated for 0.60 W at 200 mA and is placed in series with a variable resistor. Only a 9.0 volt battery is
    available to power it. To what value should the variable resistor be set to power the bulb correctly?



                                                                                     Bulb needs only 3 V

                                                                                     Bulb has resistance of 15 Ω at rated
                                                                                     power

                                                                                     Added resistance should be 30
                                                                                     ohms


                                                                                                                            4
                                    The Use of Sensors in Circuits                          IB 12

1. Light-Dependent Resistor (LDR) or Light Sensor: A photo-conductive cell made of
   semiconducting material whose resistance decreases as the intensity of the incident light increases.
                                                                         Automatic light switch
   Describe how the LDR activates the light switch.

   As ambient light decreases, resistance of LDR increases

   Potential difference across LDR increases

   Switch needs minimum PD to turn on

   When light intensity drops to desired level, PD is high
   enough to turn on switch




2. Negative Temperature Coefficient (NTC) Thermistor or Temperature Sensor: A sensor
   made of semiconducting material whose resistance decreases as its temperature increases.
                                                                               Fire alarm
   Describe how the NTC thermistor activates the fire alarm.


      As external temperature increases, resistance of NTC
      decreases

      Potential difference across R2 increases

      Switch needs minimum PD to turn on

      When temperature increases to desired level, PD is high
      enough to turn on switch




3. Strain Gauge or Force Sensor: A long thin metal wire whose resistance increases as it is
   stretched since it becomes longer and thinner.

   Describe how the strain gauge can measure the strain put on a
   section of an airplane body.


     As strain increases, resistance of strain gauge increases

     Potential difference across R2 decreases

     Voltmeter can read change in voltage which can be used
     to determine amount of strain on part




                                                                                                 5
                                 Combination Series-Parallel Circuits                                            IB 12
1. Determine the current through and the voltage drop across each resistor.




2. The battery has an emf of 12 V and negligible internal resistance and the voltmeter has an internal resistance of 20 kΩ.
    Determine the reading on the voltmeter.




  3. A cell with negligible internal resistance is connected to three resistors as shown. Compare the currents in each
      part of the circuit.




                                                                                                                         6
                                                                                                                IB 12
4. Determine the current through and the voltage drop across each resistor.




5. A battery with emf E and negligible internal resistance is connected in a circuit with three identical light bulbs.

   a) Determine the reading on the voltmeter when the switch is open and when it is closed.

    b) State what effect closing the switch has on the current through each bulb and the brightness of each bulb.




                                                                                                                     7
                                                      Ohm’s Law                                                   IB 12

Resistance: ratio of potential difference applied across a piece of material                           Formula:
to the current through the material                                                                    R=V/I




                                                                                                      Relationship:
Ohm’s Law: for a conductor at constant temperature, the current flowing
                                                                                                         VαI
through it is proportional to the potential difference across it




Ohmic Device:          a device that obeys Ohm’s law for a wide range of potential differences


Meaning: a device with constant resistance                                   Example: resistor



1. On the axes at right, sketch the I-V characteristics for a resistor.

       Resistance:

       a) R = V/I at any point


       b) related to slope of graph

       (Reciprocal = resistance)




2. A resistor is connected to two 1.5 volt cells and has 0.40 ampere of current flowing through it.

       a) Calculate the resistance of the resistor.

                   R = V/I
                   R = 7.5 Ω


       b) If the voltage is doubled, what is the new current?

       V = IR for resistor
       Resistance is constant so double current




                                                                                                                      8
                                                                                                               IB 12
    Non-Ohmic Device: a device that does not obey Ohm’s law


    Meaning: resistance is not constant                             Example: filament lamp


1. On the axes at right, sketch the I-V characteristics for a filament lamp.
         Resistance:

         a) R = V/I at any point


         b) as current increases, wire filament heats up and
         resistance increases


         c) Resistance is NOT related to the slope


         d) except in initial linear region


  2. A flashlight bulb is connected to two 1.5 volt cells and has 0.40 ampere of current flowing through it.
         a) Calculate the resistance of the bulb.

                    R = V/I
                    R = 7.5 Ω


         b) If the voltage is doubled, what is the new current?
         V = IR for bulb but resistance is not 7.5 ohms any
         more – R increases with T so less than double current




3. Discuss how the resistance varies with increasing potential difference for devices X, Y, and Z.


           X: resistance increases - ratio V/I increases

           Y: resistance is constant – ratio V/I is
           constant

           Z: resistance decreases – ratio V/I
           decreases




                                                                                                                  9
                   Using a Potentiometer to Measure I-V Characteristics                                  IB 12
  Potentiometer: a type of variable resistor with three contact points

  Common use: as a potential divider to measure the I-V characteristics of a device

The schematic shows how a potentiometer can be used as a potential divider to measure the I-V characteristics of a
filament lamp. It is placed in parallel with the lamp and the slider (center contact point) effectively splits the
potentiometer into two separate resistors AB and BC. By moving the slider, the ratio of the voltage drops across the
resistors AB and BC is varied.
                                                     Redraw the schematic with an ammeter and a voltmeter correctly
                                                     placed to measure the I-V characteristics of the filament lamp.




    Comment on the circuit characteristics as the slider is moved from A to B to C.

    Slider at A:




    Slider at B:




    Slider at C:




                                                                                                             10
                                                                                                 IB 12
                              Internal Resistance of Batteries

A 6 volt battery is connected to a variable resistor and the current in the circuit and potential difference
across the terminals of the battery are measured over a wide range of values of the resistor. The results
are shown in the table.
                                                                  Predicted        Actual        Voltage across
                                               Resistance (Ω)
                                                                 Current (A)     Current (A)      battery (V)
                                                   2000            0.003            0.003            6.00
                                                    200             0.03             0.03            5.99
                                                     20              0.3             0.29            5.85
                                                      2                3              2.4            4.80
                                                     0.2              30              8.8            1.71
                                                    0.02             300             11.5            0.23
                                                   0.002            3000             12.0            0.02
                                                  0.0002           30000             12.0            0.00

Why does the current seem to be limited to a maximum of 12.0 amperes and why does the voltage
across the battery not remain constant at 6.0 volts?

 The battery has some internal resistance. As the
 external resistance decreases, more and more of the
 energy supplied by the battery is used up inside the
 battery.


 Electromotive force (emf): total energy per unit charge supplied by the battery               Symbol: ε or E

                                                                                               Units: V = J/C

 Terminal Voltage (Vterm): potential difference across the terminals of the battery


 Ideal Behavior: Vterm always equals emf since no internal resistance

 Real Behavior:

     1) Think of battery as internal E and tiny internal resistor r


     2) Vterm only equals the emf when no current is flowing


     3) E is split between R and r


     4) When R>>r, Vterm ≈ emf


     5) As R decreases, Vr increases and VR decreases
                                                                                                   11
                                                                                                              IB 12
                                                               Relationship between emf and terminal voltage

                                                                  Treat internal resistance as a series resistor

                                                                                      ε = I RT

                                                                                    ε = I (R + r)

                                                                                    ε = IR + Ir

                                                          Note that in the absence of internal resistance, ε = Vterm


1. A resistor is connected to a 12 V source and a switch. With the switch open, a voltmeter reads the potential difference
  across the battery as 12 V yet with the switch closed, the voltmeter reads only 9.6 V and an ammeter reads 0.40 A for the
  current through the resistor. Sketch an appropriate circuit diagram and calculate the internal resistance of the source.




2. Discuss the expected I-V characteristics for this battery and how they can be
    experimentally determined.


  R can be adjusted from 0 to its max value

  A graph of Vterm vs. I can be drawn

  Specific equation of graph can be compared to math model to derive
  internal resistance

  Emf = Vterm + Ir

  Vterm = -Ir + emf      so slope = -r and y-intercept = emf




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