Current Electricity and Elastic Properties

Contents Current Electricity Elastic Properties of Solids 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 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) V I R Resistance = Voltage / Current R = V / I Unit of resistance: Ohm, Ω

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 V I V I V 1. Wire 2. Bulb 3. Diode - + A V A potential divider is used to investigate how the current passing in a component is dependant on the voltage across it.

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 = n A e v e=electronic charge For a non-metal: I = n A q v 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. a.c. changes direction, while d.c maintains the same direction even though the current value may vary Current d.c. Time a.c.

Under Stress Hooke’s Law F = ke “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 Elastic Properties of Solids Ohm’s Law, Resistance and Resistivity Energy Transfer in Circuits Resistance in Circuits Alternating Current Elastic Properties of Solids Under Stress