Physics 232C Topic 17a Electric Current Physics 232C Key Concepts Electric Current Key Concepts Electric Current resistance and Circuits resistance and Circuits Electric Current and Resistance Ohm s law Resistivity and temperature dependence Power Batteries and Kirchhoff s Rules Real and Ideal batteries Junction Rule Loop Rule Combining Resistors Series Parallel RC Circuits Time dependence Physics 232C 1 2 1 Properties of current Properties of current Charges flowing in a wire a current carrying wire Charged plates Physics 232C Properties of current Properties of current A compass needle is deflected when placed close to a current carrying wire 3 4 We ll talk about this later Physics 232C 2 Definition of current Definition of current The positive direction of current flow is the direction of motion of positive charge I E I E causes charges to move in the wire Electrons are the carriers that move but Positive current is in the direction of E Opposite the direction of electron movement In the direction in which a positive charge will move Physics 232C In other words In other words Current I is moving charge High V A Low V Current amount of charge q that flows through an area A divided by the time interval t Units for current Amperes or Amps A I q t A C s Physics 232C 5 6 3 Conservation of Current Conservation of Current Charge is conserved Current is moving charge so it s also conserved Current is the same at all points in a current carrying wire A lightbulb doesn t use up the current but it does use energy filament gets hotter and glows Current at point A Current at point B Physics 232C I A I B Physics 232C Topic 17b Electric Current a Microscopic View Physics 232C 7 8 4 Electric current microscopic view Electric current microscopic view When electrons move through a wire they undergo many collisions The actual path may look like High V Low V Due to the collisions the velocity on average is constant drift The drift velocity of the electrons is actually very slow less than velocity vdrift 1 meter per hour Q So how can we have high currents A Because there are so many electrons Physics 232C 9 Microscopic View 2 Microscopic View 2 v d The average electron speed is vdrift t Consider one electron at point x After time t it will have moved a distance l vdrift t All the mobile electrons will have moved over a distance l l l Physics 232C 10 5 Microscopic View 3 Microscopic View 3 The volume of the cylinder vol Avdrift t l vol lA If n number of mobile electrons per unit volume n is the number density n for copper is 8 48 1028 m 3 The number of electrons moved is N vol nAvdrift t The charge q that has moved must be the of electrons moved times the charge of an electron e q nAvdrift t e Therefore the current is I q t nAvdrifte Physics 232C 11 Microscopic View 4 Microscopic View 4 Lastly we can rewrite the expression using current density j I A j I A nvd e Physics 232C 12 6 Physics 232C Topic 17c Ohm s Law Resistivity and Temperature Dependence Physics 232C 13 Resistance and Ohm s Law Resistance and Ohm s Law The current is determined by the potential difference V Vbattery in this case and the resistance R of the wire VI R VR I The units of R are Ohms V decreases Vbattery V A Physics 232C 14 7 Ohm s Law Ohm s Law V2 V1 I V V2 V1 If V is the voltage difference across a circuit element of resistance R and current I then V IR VI R VR I OHM S LAW Physics 232C 15 Circuit Diagrams Circuit Diagrams Two equivalent ways resistors and batteries are shown in circuit diagrams Physics 232C 16 8 Ohmic and Non Ohmmic Ohmic and Non Ohmmic Materials like resistors that obey Ohm s law are Ohmic materials V is proportional to I Semiconductors are non ohmic Non Linear Ex Light emitting diodes LED Physics 232C 17 Resistivity 1 Resistivity 1 The resistance of a wire depends on its length L and cross sectional area A I V R A L Physics 232C 18 9 Resistivity 2 Resistivity 2 The resistance of a wire also depends on the resistivity of the material I V R Compare to capacitors C 0A d Q CV Physics 232C 19 Temperature dependence of Temperature dependence of resistivity resistivity 0 As the temperature of a material increases its resistivity increases and hence its resistance increases by the following relations 0 1 T T0 R R0 1 T T0 temperature coefficient of resistivity The units of are 1 C or 1 K Physics 232C 20 T0 room temp T Not all materials have positive temperature coefficients of resistivity some have negative coefficients 10 Resistivities Temperature coefficients Resistivities Temperature coefficients Metals have low resistivity and are good conductors Materials with high resistivity are good insulators Resistance of wires Resistance of wires Semiconductors have negative temperature coefficients Physics 232C 21 For the rest of the course unless otherwise noted we assume that all wires are ideal wires with no resistance Since R 0 Ohm s law gives Vwire IRwire 0 Physics 232C 22 11 Physics 232C Example 17c Current in a Wire Physics 232C 23 Current in a Wire Current in a Wire 1 A number 14 copper wire has a diameter of 1 628 mm Calculate the resistance of a 31 0 m long piece of such wire Use 1 72 10 8 m for the resistivity of copper 2 For safety the National Electrical Code limits the allowable amount of current which such a wire may carry When used in indoor wiring the limit is 15 0 A for rubber insulated wire of that size What would be the voltage between the ends of the wire 3 What is the current density in the wire when it is carrying the maximum allowable current 4 What is the drift velocity of the electrons when the wire is carrying the maximum allowable current The density of electrons in copper is 8 47 1028 m 3 Physics 232C 24 12 Physics 232C Topic 17d Work Energy and Power Physics 232C 25 Work Energy and Power Work Energy and Power Remember from mechanics PHY231 Work W Fdcos units are joules J Nm Power P W t units are watts W J s When a resistor gets hot it must be dissipating giving off energy What is the power dissipated by a resistance R Physics 232C 26 13 Work Energy and Power 2 Work Energy and Power 2 Power dissipated as heat by resistance R Let s start by considering work W U Q V Now power V R IV R WP t R QV R t P R Q t IV R Physics 232C 27 Power and Energy in Circuits Power and Energy in Circuits Lets look at the power dissipated by a light bulb with resistance R Here let s assume that the wires have negligible zero resistance The …