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Current Electricity and Elastic Properties
ContentsCurrent ElectricityOhms Law, Resistance and ResistivityEnergy Transfer in CircuitsResistance in CircuitsAlternating CurrentElastic Properties of SolidsUnder Stress
Ohms Law, Resistance and ResistivityResistance
Current, Iflow of electrons around the circuit(Amps)(how fast the electrons travel around)
Voltage, VDriving force that pushes electrons(Volts)(electrical pressure)
Resistance, RSlows down the electrons(Ohms)(resists the flow of the electrons)Resistance = Voltage / Current R = V / I Unit of resistance: Ohm,
Ohms Law, Resistance and Resistivity1. Wire3. Diode2. BulbThe graphs below represent typical results obtained for a metal wire at constant temperature, a filament lamp, and a diode.- +A potential divider is used to investigate how the current passing in a component is dependant on the voltage across it.
Ohms Law, Resistance and ResistivityResistivityunit: Ohm metres, m
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 / AThe resistive properties of a resistor are measured by its resistivity, When this is taken into account, the formula becomes: R = L / A where L = length of material, A = cross sectional area
Energy Transfer in CircuitsCharge Unit: Coulomb, CThe coulomb is the charge that flows past a point when a steady current of 1A passes for 1 secondDrift VelocityThe 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, AFor a metal:I = n A e v e=electronic chargeFor a non-metal:I = n A q v q=ionic charge
Resistance in CircuitsSeriesR = R1 + R2 + R3 ...Parallel 1/R = 1/R1 + 1/R2 + 1/R3 ...Internal ResistanceA cell in a circuit has its own internal resistance, r. The greater the cells current the more work is done against the cells internal resistance, and therefore less can be done on the external circuit.e.m.f = terminal p.d. + p.d. across internal resistanceE = V + Ir
Resistance in CircuitsKirchoffs 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 junction2nd 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 = IR4.9A1.4A1.2A2.3AAn example of a closed loop
Alternating Current and the OscilloscopeAlternating and Direct DirectA current from a battery is direct current, d.c., while mains electricity is alternating current, a.c.
a.c. changes direction, while d.c maintains the same direction even though the current value may varyd.c.a.c.TimeCurrent
Under StressHookes LawForces 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 = keWhere: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 StressElastic Potential EnergyIf 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 StressStress, strain and Youngs Modulus
Stress is defined as the force per unit area of a material:Stress = force / cross sectional areawhere 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 lengthwhere e = strain lo = the original length e = extension = (l-lo) and l = stretched lengthStrain has no units because it is a ratio of lengths.The gradient of the straight-line graph is the Youngs modulus, E
Units of the Young modulus E: Nm-2 or Pa
SummaryCurrent ElectricityOhms Law, Resistance and ResistivityEnergy Transfer in CircuitsResistance in CircuitsAlternating CurrentElastic Properties of SolidsUnder Stress