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Current & Resistance. - Current and current density Ohm’s Law Resistivity Resistance. Electrical Current. CURRENT I is the amount of positive charge flowing past a fixed point in the wire per unit time : if charge dQ flows in time dt

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## Current & Resistance

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**Current & Resistance**• - Current and current density • Ohm’s Law • Resistivity • Resistance**Electrical Current**CURRENTI is the amount of positive charge flowing past a fixed point in the wire per unit time : if charge dQ flows in time dt Units: 1 ampere (A) = 1 C/s Direction: by convention, current is the direction of movement of positive charge + + + - - - - - - + + + I I**Electron Velocities**• Random velocities of electrons are large (several km/s) • Drift velocity is a slow, average motion parallel to E + no field E end end start start net displacement**+**+ + + + + E + + + + + + L = vdDt Determining the current Charge ΔQ in length L of wire passes through the shaded disk of area A in time Δt : ΔQ = (number of charge carriers/volume) x (charge on each one) x volume**Charge: DQ = n q V**= n q (AL) = n q A vdDt (since L=vt) Current: I = DQ/Dt = nqAvdDt /Dt I = nqAvd So, vd = average (“drift”) velocity of each charge q = charge on each particle n = number of charge carriers per unit volume A = cross section area L = length AL = volume**The mobile charges in most metals are electrons, with about**one or two electrons per atom being free to move. So there are about 1023 charges per cm3 (or 10 29 m-3). Example Take Area = 1 mm2, assume I = 1 A Which way are the electrons moving?**E = 0 inside ?**Note: in electrostatics, we had E=0 inside a conductor, if not, charges would move, the conductor would not be in equilibrium and there would be a current. For a wire to carry a current, we must have an electric field inside the conductor, which is caused by the potential difference between the ends of the wire. This is no longer electrostatics!**Example**A copper wire of cross sectional area 3x10-6 m2 carries a current of 10A. Find the drift velocity of the electrons in this wire. Copper has a density of 8.95g/cm3, and atomic weight of 63.5g/mole. Avagadro’s number is 6.02x1023 atoms. Assume each atom contributes one free electron.**Questions**• When you turn on a flashlight, how long does it take for the electrons from the battery to reach the bulb? • What happens to the wire as the electrons go through it? • If you double the electric field in the wire, does the acceleration of the electrons double? • If the electric field remains constant, how do the electron kinetic energies change with time?**Current Density J**The current density is defined as the current per unit area in a conductor, where A is the cross section of conductor. The current density is a vector quantity, units: Amps/m2. And since I=nqAvd; Where is a constant called the conductivity of the material. The current density J and the electric field E are bothestablished in a conductor as a result of a potential difference across the conductor.**A**E Because J is proportional to the field, current in a wire is proportional to the potential difference between the ends of the wire. L Uniform E “Resistance”, R**RESISTIVITY: the inverse of conductivity.**(this depends on the type of material) Ohm’s Law (Uniform wire, Length L, cross-section area A) where Unit of resistance R is:**Ohm’s Law**• Current density field: J = sE • Current potential difference: V = IR r = “resistivity”, has units of W m s = “conductivity” units,**Resistivities of a few materials**ρ (20°C) (Ω·m) Cu 1.7 x 10-8 Al 2.8 x 10-8 Graphite 3500 x 10-8 Si 640 Quartz ~ 1018**Example**A copper wire, 2 mm in diameter and 30 m in length, has a current of 5A. Find: a) resistance b) potential difference between the ends c) electric field d) current density**Quiz**The wire in the previous example is replaced with a wire of the same length and half the diameter, carrying the same current. By what factor will each of the following change? • resistance • potential difference between the ends • electric field • electron number density • electron drift speed • current density**Summary**Current Density: Conductivity: Resistivity: Resistance: Ohm’s Law:

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