Current Electricity and Elastic Properties by jal11416

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									Current Electricity and
  Elastic Properties
                     Contents
   Current Electricity
    – Ohm’s Law, Resistance and Resistivity
    – Energy Transfer in Circuits
    – Resistance in Circuits
    – Alternating Current
   Elastic Properties of Solids
    – Under Stress
        Ohm’s Law, Resistance and
                Resistivity
Resistance

   Current, I      flow of electrons around the circuit
    (Amps)          (how fast the electrons travel around)
   Voltage, V      Driving force that pushes electrons
    (Volts)         (electrical pressure)
   Resistance, R   Slows down the electrons
    (Ohms)          (resists the flow of the electrons)


Resistance = Voltage / Current                  V
     R      =    V     /   I
  Unit of resistance: Ohm, Ω                I       R
         Ohm’s Law, Resistance and
                 Resistivity
The graphs below represent typical results obtained for a metal
wire at constant temperature, a filament lamp, and a diode.

         I                    I                   I


                 V                   V                        V

       1. Wire             2. Bulb            3. Diode
                                                      -   +


 A potential divider is used to investigate
 how the current passing in a component       A

 is dependant on the voltage across it.
                                                          V
          Ohm’s Law, Resistance and
                  Resistivity
Resistivity                unit: Ohm metres, Ωm
The physical dimensions and the cross sectional area have a
direct effect on the resistance of a resistor.
The resistance of a sample of material is directly
proportional to the length and inversely proportional to
its cross sectional area.
Hence:                  R   I/A

The resistive properties of a resistor are measured by its
resistivity, ρ
     When this is taken into account, the formula becomes:
                          R = ρL / A
     where L = length of material, A = cross sectional area
       Energy Transfer in Circuits
Charge               Unit: Coulomb, C
“The coulomb is the charge that flows past a point when a
steady current of 1A passes for 1 second”

Drift Velocity
The electrons in a current have an overall motion at low
speed in a direction negative to the positive.
The three things that affect the drift velocity are:
• Current, I
• Charge carrier concentration, n : number of charge
carrying electrons per unit volume
• Cross sectional area of material, A
For a metal:        I=nAev         e=electronic charge
For a non-metal:    I=nAqv         q=ionic charge
                  Resistance in Circuits
Series
                          R = R1 + R2 + R3 ...


Parallel
                     1/R = 1/R1 + 1/R2 + 1/R3 ...


Internal Resistance
A cell in a circuit has its own internal resistance, r. The greater the cell’s
current the more work is done against the cell’s internal resistance, and
therefore less can be done on the external circuit.
     e.m.f = terminal p.d. + p.d. across internal resistance
                           E = V + Ir
              Resistance in Circuits
Kirchoff’s Laws are Conservation Rules of a circuit

1st Law: “The total current that enters a junction is equal to
          the total current that leaves the junction”
                            1.4A

                     4.9A   1.2A

                            2.3A



2nd Law: Conservation of energy. “Around any closed loop
        (i.e. complete series path), the total e.m.f. is equal
        to the sum of the p.d.’s, E = ΣIR


                                   An example of a closed loop
        Alternating Current and the
                Oscilloscope
Alternating and Direct Direct
A current from a battery is direct current, d.c., while mains
electricity is alternating current, a.c.
             Current                 d.c.

                                               Time
                                            a.c.


a.c. changes direction, while d.c maintains the same direction
          even though the current value may vary
                             Under Stress
Hooke’s Law
“Forces can cause objects to deform (i.e. change their shape). The way in
which an object deforms depends on its dimensions, the material it is
made of, the size of the force and direction of the force.”
                                        F = ke
Where:
F = tension acting on the spring.
e is extension = (l-lo); l is the stretched length and lo is original length, and.
k = the spring constant.
                                Once the spring is extended beyond the point P, it
                                will no longer return to its original shape. This is the
                                point of elastic limit.

                                If a material returns to its original shape after forces
                                are applied, it demonstrates elastic behaviour.

                                If a material deforms from its original shape after
                                forces are applied, it is a sign of plastic behaviour.
                          Under Stress
Elastic Potential Energy
“If the deformation caused is within the elastic limit, the work done in
deforming the object is stored within it as potential energy. This is called
(elastic) ‘strain energy’. When the applied force is removed the energy is
released. The strain energy then performs work in changing the object
and to its original state.”




      The work done (W) by the object is
      the shaded triangular area under
      the straight line
                             Under Stress
Stress, strain and Young’s Modulus
             Stress is defined as the force per unit area of a material:
                      Stress = force / cross sectional area
               where s = stress F = force applied, A= cross sectional area
                               Units of s : Nm-2 or Pa.
                   Strain is defined as extension per unit length.
                         Strain = extension / original length
 where e = strain lo = the original length e = extension = (l-lo) and l = stretched length
                Strain has no units because it is a ratio of lengths.

                                  The gradient of the straight-line graph is the
                                  Young’s modulus, E




                                  Units of the Young modulus E: Nm-2 or Pa
                     Summary
   Current Electricity
    – Ohm’s Law, Resistance and Resistivity
    – Energy Transfer in Circuits
    – Resistance in Circuits
    – Alternating Current
   Elastic Properties of Solids
    – Under Stress

								
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