Physics 2102 Gabriela Gonz lez Georg Simon Ohm 1789 1854 E In a conductor electrons are free to move If there is a field E inside the conductor F qE means the electrons move in a direction opposite to the field this is an electrical current We think of current as motion of imaginary positive charges along the field directions Andre Marie Ampere 1775 1836 E Wasn t the field supposed to be zero inside conductors Yes if the charges were in equilibrium The reasoning was electrons move until they cancel out the field If the situation is not static that is if electrons are moving then the field can be nonzero in a conductor and the potential is not constant across it However somebody has to be pumping the electrons this is the job of the battery we put across a circuit If there is no source creating the electric field the charges reach equilibrium at E 0 Current is a scalar NOT a vector although we use arrows to indicate direction of propagation Current is conserved because charge is conserved junction rule everything that comes in must go out Electrons are not completely free to move in a conductor They move erratically colliding with the nuclei all the time this is what we call resistance The resistance is related to the potential we need to apply to a device to drive a given current through it The larger the resistance the larger the potential we need to drive the same current Ohm s laws Georg Simon Ohm 1789 1854 a professor who preaches such heresies is unworthy to teach science Prussian minister of education 1830 Devices specifically designed to have a constant value of R are called resistors and symbolized by The current is the flux of the current density If surface is perpendicular to a constant electric field then i JA or J i A J dA E Units i Drift speed vd Velocity at which electrons move in order to establish a current L Charge q in the length L of conductor n density of electrons e electric charge A E i Where is the current current density electron density drift velocity electric field largest Metal field lines These two devices could have the same resistance R when measured on the outgoing metal leads However it is obvious that inside of them different things go on resistivity Resistivity is associated resistance R V I with a material resistance with respect to a device constructed with the material Example A L V Makes sense For a given material Resistivity depends on temperature 0 1 T T0 At what temperature would the resistance of a copper conductor be double its resistance at 20 0 C Does this same doubling temperature hold for all copper conductors regardless of shape or size b a A battery pumps charges through the resistor or any device by producing a potential difference V between points a and b How much work does the battery do to move a small amount of charge dq from b to a dW dU dq V dq dt dt V iV dt The battery power is the work it does per unit time P dW dt iV P iV is true for the battery pumping charges through any device If the device follows Ohm s law i e it is a resistor then V iR and P iV i2R V2 R b The battery operates as a pump that moves positive charges from lower to higher electric potential A battery is an example of an electromotive force EMF device a These come in various kinds and all transform one source of energy into electrical energy A battery uses chemical energy a generator mechanical energy a solar cell energy from light etc i d b c The difference in potential energy that the a device establishes is called the EMF i and denoted by E Va E iR Va E iR Va iR E a b c d a b Given the emf devices and resistors in a circuit we want to calculate the circulating currents Circuit solving consists in taking a walk along the wires As one walks through the circuit in any direction one needs to follow two rules a When walking through an EMF add E if you flow with the current or E otherwise How to remember current gains potential in a battery When walking through a resistor add iR if flowing with the current or iR otherwise How to remember resistors are passive current flows potential down Example Walking clockwise from a E iR 0 Walking counter clockwise from a E iR 0 Current and current density i dq dt i J dA J nevd Resistance and resistivity V iR E J R L A 0 1 T T0 Power P iV V2 R i2R Walking a circuit E iR 0 A human being can be electrocuted if a current as small as 50 mA passes near the heart An electrician working with sweaty hands makes good contact with the two conductors he is holding If his resistance is 1500 what might the fatal voltage be Ans 75 V Two conductors are made of the same material and have the same length Conductor A is a solid wire of diameter 1 0 mm Conductor B is a hollow tube of outside diameter 2 0 mm and inside diameter 1 0 mm What is the resistance ratio RA RB measured between their ends A R L A B AA r2 AB 2r 2 r2 3 r2 RA RB AB AA 3 A 1250 W radiant heater is constructed to operate at 115 V a What will be the current in the heater b What is the resistance of the heating coil c How much thermal energy is produced in 1 0 h by the heater Formulas P i2R V2 R V iR Know P V need R to calculate current P 1250W V 115V R V2 P 115V 2 1250W 10 6 i V R 115V 10 6 10 8 A Energy P dU dt dU P dt 1250W 3600 sec 4 5 MJ A 100 W lightbulb is plugged into a standard 120 V outlet a What is the resistance of the bulb b What is the current in the bulb c How much does it cost per month to leave the light turned on continuously Assume electric energy costs 6 kW h d Is the resistance different when the bulb is turned off Resistance same as before R V2 P 144 Current same as before i V R 0 83 A We pay for energy used kW h U Pt 0 1kW 30 24 h 72 kW h 4 32 d Resistance should be the same but it s not resistivity and resistance increase with temperature When the bulb is turned off it is colder than when it is turned on so the resistance is lower a b c d e f Which light bulb has a smaller resistance a 60W or a 100W one Is the resistance of a light bulb different when it is on and off Which light bulb has …
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