Current & ResistanceElectric currentlon-capa Electric current IIelectric current III: what really happenselectric current IVquestionwait a second…batteriesA simple circuitquestionhow to measure current?how to measure voltage?Resistance IResistance IIResistance IIIOhm’s law and resistivityOhm’s lawquestiona resistor bank..lon-capaquestiontemperature dependence of resistivitysuperconductorsquestionlon-caparesistors in a circuitquestionresistors on circuit boardsthe lightbulbelectrical energy and powerquestionquestionlon-capaCurrent & ResistancePHY232Remco [email protected] W109 – cyclotron buildinghttp://www.nscl.msu.edu/~zegers/phy232.htmlPHY232 - Remco Zegers - Current & Resistance 2Electric current¾ Although we have mostly looked at static electric phenomena, we already saw that charge can move and hence produce a current.A++++Current=amount of charge ΔQ that flows through an area Adivided by the time interval Δt:PHY232 - Remco Zegers - Current & Resistance 3lon-capa¾ do problems 1,2 of set 3PHY232 - Remco Zegers - Current & Resistance 4Electric current II¾ A matter of convention:¾ The direction of current is the direction in which positivecharges flow, even the flow is often of electrons (negative)¾ Remember: positive charge moves from a region of high potential to low potential+-High VLow VHigh VLow VPHY232 - Remco Zegers - Current & Resistance 5electric current III: what really happens¾ When electrons move through a wire they undergo many collisions and a typical path looks like:¾ Because of the collisions, the velocity is on average constant¾ The drift velocity of the electrons is actually very slow (less than 1 meter per hour). So why can we have high currents?High VLow VBecause there are so many electrons!!!demo: model of resistancePHY232 - Remco Zegers - Current & Resistance 6electric current IV¾ let’s assume the average electron speed is v¾ consider one electron at point x¾ after time t it will have moved….¾ a distance l=vt¾ in fact all the electrons over the distance l will have moved¾ the volume of the cylinder V=Al=Avt¾ if n: number of electrons per unit volume, the number of electrons moved is: nV=nAvt¾ the charge ΔQ that has been moved: nAvtq¾ current I= ΔQ/t=nAvq-PHY232 - Remco Zegers - Current & Resistance 7question¾ A current of 1 A is running through a Copper wire with cross section1mm2. Each Copper atom produces 1 free electron. a) How many free charge carriers per unit volume are there? (Given that the molar mass of Cu is 63.5 g and the density of copper is8.92 g/cm2). b) What is the drift velocity?PHY232 - Remco Zegers - Current & Resistance 8wait a second…¾ Wasn’t charge supposed to be collected on the surface of a conductor?¾ a) Yes, the previous slides were nonsense¾ b) Yes, but that was only for a static system (no electrons moving)¾ c) No, that only holds for excess charge, I.e. if there are more electrons than can be delivered by the atomsPHY232 - Remco Zegers - Current & Resistance 9batteries¾ A battery can produce a potential difference between the anode (negative) and cathode (positive). When connected(I.e. using a wire or via a device) currentcan flow.¾ The charge is created through chemicalreactions. Once the chemical fuel isused, the battery is empty¾ commonly used are zinc-carbon batteries: for the chemists: see http://en.wikipedia.org/wiki/Zinc-carbon_batteryPHY232 - Remco Zegers - Current & Resistance 10A simple circuitPower sources can be DC (Direct Current) or AC (AlternatingCurrent). We will deal with DC circuits firstOFFONA basic electric circuit consists of apower source (e.g. a battery) in which the + and – side are connected via a wire and some devices.As long as the circuit is open, nocurrent will flow and hence thedevices not work.PHY232 - Remco Zegers - Current & Resistance 11question¾ Which of the following lights will not shine after the switches are closed?1234a) 2b) 2,3c) 2,3,4d) 1,2,3,4PHY232 - Remco Zegers - Current & Resistance 12how to measure current?¾ The current anywhere between A and B must be constant, else electrons would accumulate at a certain point in the line¾ A device to measure current in the light should therefore be placed in line (in series) with the light¾ The device is called an Ampere meter1AB1ABPHY232 - Remco Zegers - Current & Resistance 13how to measure voltage?¾ To measure the voltage over the light, realize that we in fact need to measure the potential difference between A and B¾ A device to measure voltage over the light bulb should therefore be placed in parallel with the light¾ The device is called a Volt meter1A B1A BPHY232 - Remco Zegers - Current & Resistance 14Resistance I¾ When electrons move through a material, they undergo many collisions which hinders the motion (like friction).¾ Without such collisions, the electrons would accelerate (since there is a force acting on them)¾ The resistive force counterbalances the electric force so the drift velocity is constant ¾ When the resistive force is high, the current will go down if the voltage difference that drives the motion remains the same.High VLow VPHY232 - Remco Zegers - Current & Resistance 15Resistance IICompare with water flow through a pipe. If the pipe becomes narrow, flow is reduced. If the length over whichthe pipe is narrow becomes longer, flow is further reduced.so resistance R :high pressurelow pressureflowPHY232 - Remco Zegers - Current & Resistance 16Resistance III¾ voltage is the “equivalent” of pressure and current the equivalent of flow¾ If pressure (voltage) difference increases, the flow (current) will increase¾ If the resistance increases, the flow current will go down if the pressure difference remains the samehigh pressurelow pressureflow+ -VIPHY232 - Remco Zegers - Current & Resistance 17Ohm’s law and resistivity¾ Ohm’s law¾ For a specific material, the resistance R can be calculated using:¾ where R: resistance (in V/A=Ω (Ohm)), ρ the resistivity (material dependent in Ωm), l the length of the object and A the cross section of the objectdemo: Jacob’s ladderPHY232 - Remco Zegers - Current & Resistance 18Ohm’s law¾ Ohm’s law implies that V~I which is true for many materials but not for all:Ohmic resistanceNon-ohmic resistancePHY232 - Remco Zegers - Current & Resistance 19question¾ A voltage of 100V is put over a thick wire of unknown material. The current is measured is 4.5x103A. The cross section of the wire is 1cm2and the