5 Electric CurrentElectric current is the rate of flow of charge through a cross sectional areaThe SI unit of current is the ampere (A)1 A = 1 C / sThe symbol for electric current is I
6 Average Electric Current ΔQ is the amount of charge that passes through A in time ΔtAssume charges are moving perpendicular to a surface of area AInstantaneous Electric Current
7 Direct Current DC Alternating Current AC Provided by batteries Provided by power companies
8 Microscopic View of Current: While the switch is open: Free electrons (conducting electrons) are always moving in random motion.The random speeds are at an order of106 m/s. The sharp changes in direction are due to collisionsThere is no net movement of charge across a cross section of a wire.
9 What occurs in a wire when the circuit switch is closed?
10 What occurs in a wire when the circuit switch is closed? An electric field is established instantaneously (at almost the speed of light, 3x108 m/s).Free electrons, while still randomly moving, immediately begin drifting due to the electric field, resulting in a net flow of charge.Average drift velocity is about 0.01cm/s.
11 Electrons flow in a net direction away from the (-) terminal. Closing the switch establishes a potential difference (voltage) and an electric field in the circuit.High PotentialLow PotentialElectrons flow in a net direction away from the (-) terminal.
12 Conventional current has the direction that the (+) charges would have in the circuit.
13 A Battery Provides Energy The battery “pumps” positive charges fromlow (-) tohigh (+) potential.Electric Circuit
14 Resistors use up Energy When the current goes through the resistor it goes to a lower potential.Electric Circuit
15 Charge Carrier Density, n: number of charge carriers per unit volume Charged particles (current carriers)move through a conductor of cross-sectional area AVolume = A ΔxTotal number of charge carriers= n A Δx
16 Current in terms of Drift Speed Iav = ΔQ/Δt = nqvdA or for a charge of an electron: Iav =nevdA Derivation:ΔQ = (nA Δx)qDrift speed, vd, is the speed at which the carriers move: vd = Δx / ΔtΔQ = (nAvd Δt)q
17 Question:If the drift velocity is about 0.01cm/s, why do the lights turn on instantaneously when the circuit switch is closed?What is required in order to have an electric current flow in a circuit?
18 Question: Why is the bird on the wire safe? Question: Why do electricians work with one hand behind their back?
19 Question: Why is the ground prong longer than the other two in a plug? Question: Why is there a third rail for the subway?
20 Resistance, RResistance of an object to the flow of electrical current.Resistance in a circuit is due to collisions between the electrons carrying the current with the fixed atoms inside the conductorR= V / IResistance equals the ratio of voltage to current.Unit: Ohm (Ω)
21 Ohm’s Law (Georg Ohm, 1787-1854) V = IR The voltage , V, across a resistor is proportional to the current, I, that flows through it.In general, resistance does not depend on the voltage. (but for non-Ohmic resistors it may.)Applies to a given resistor or equivalent combination.The voltage is the potential difference across the resistor or equivalent combination.
23 Ohmic Resistor The relationship between current and voltage is linear A device that obeys Ohm’s Law, who’s resistance does not depend on the voltage.Most metals obey Ohm’s lawThe relationship between current and voltage is linear
24 Nonohmic Material, Graph Nonohmic materials are those whose resistance changes with voltage or currentThe current-voltage relationship is nonlinear
25 Resistance Depends on material, size and shape, temp. R=ρ L A ρ: resistivity-Resistivity has SI units of ohm-meters (Ω . M-An ideal conductor would have zero resistivityσ: 1/ρ conductivity
26 Which has the greatest and least resistance? Ans: Greatest-D,Smallest-B
27 Temperature Dependence of Resistance and Resistivity for metals R= Ro(1 +α T)Ro : reference resistance usually at 20oC (sometimes at 0o C)α: temperature coefficient of resistivityResistivityr= r o(1 +α T)
28 Resistivity and Temperature r= r o(1 +α T) For metals, the resistivity is nearly proportional to temperatureNonlinear region at very low temperaturesResistivity reaches a finite value (residual resistivity) as the temperature approaches absolute zero
29 Semiconductors r= r o(1 +α T), a<0 For semiconductors there is a decrease in resistivity with an increase in temperatureα is negative
30 SuperconductorsFor superconductors resistances fall to close to zero below a critical temperature TCThe graph is the same as a normal metal above TC, but suddenly drops to zero at TC
31 Current Density, J: current per unit area J = I / A A current density J and an electric field E are established in a conductor,when a potential difference is applied across the conductorThe current density is a vector in the direction of the positive charge carriers
32 Current Density, J: current per unit area J = I / A = nqvdA /A J=nqvd J units: A/m2This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current
33 Ohm’s Law in terms of Conductivity J = σ E Ohm’s law states that for many materials, the ratio of the current density to the electric field is a constant σ (conductivity)that is independent of the electric field producing the current
34 Radial Resistance of a Cable, Example 27.4 In a coaxial cable the current flows along its length. Some unwanted current leaks radially. Find the radial resistance of the silicon
35 Ex.27.4 SolutionAssume the silicon between the conductors to be concentric elements of thickness dr.The total resistance across the entire thickness of silicon:
37 Derivation of Drift Velocity Electrical force acting on electron is F = qEa = F / me = qE / mevf = vi + atvf = vi + (qE/me)t For t=t the average time interval between successive collisionsvf avg = vdvd = (qE/me)t
38 Derivation of Resistivity J = nqvd = (nq2E / me)tJ=sENote, the conductivity and the resistivity do not depend on the strength of the fieldMean free path, ℓ , average distance between collisionst = ℓ/vav