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Physics 272 February 10 Spring 2015 www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm go.hawaii.edu/KO Prof. Philip von Doetinchem [email protected] PHYS272 - Spring 15 - von Doetinchem - 240 Current, drift velocity, current density ● ● Amount of charge flowing through an area: Current in a conductor is the product of the density of moving charged particles, the magnitude of charge of each such particle, the magnitude of the drift velocity, and the crosssection area PHYS272 - Spring 15 - von Doetinchem - 241 Resistivity ● ● Generally current density in conductor depends on electric field and the properties of the material as a function of temperature Ohm's law: Source: http://de.wikipedia.org/wiki/Georg_Simon_Ohm ● ● Resistivity of a material is the ratio of electric field and current density → do not confuse with resistance! The greater the resistivity the greater the field has to be to achieve the same current density PHYS272 - Spring 15 - von Doetinchem - 242 Resistivity ● Perfect conductors would have zero resistivity ● Perfect insulators have an infinite resistivity ● ● ● ● Metals have a ~1022 times smaller resistivity than insulators Inverse of the resistivity is the conductivity Ohm's law is not perfect and can only be applied for certain temperature ranges A conductor is called ohmic or linear if the resistivity in a certain temperature range does not depend on the value of the electric field PHYS272 - Spring 15 - von Doetinchem - 243 Resistivity and temperature ● ● ● ● Resistivity in a metal nearly always increases with temperature due to more vibration of the ions in the material Behavior over a small temperature range can be described by: Measuring the resistivity is a sensitive measure of temperature, e.g., thermistor use semiconductor materials Superconductivity: sudden change to zero resistivity at cold temperatures of certain materials: electrons flow freely without creating heat in the conductor PHYS272 - Spring 15 - von Doetinchem - 244 Quench of superconducting magnets at CERN PHYS272 - Spring 15 - von Doetinchem - 245 Resistance ● ● Current and potential difference are easier to measure than current density and electric field As current flow through electric potential difference → electric potential energy is lost → energy goes into the ions PHYS272 - Spring 15 - von Doetinchem - 246 Interpreting resistance ● ● ● ● Resistance is proportional to length and inversely proportional to cross-section Analogy: – a narrow hose has more resistance than a wide one – a long hose has a larger resistance than a short one Circuit device with a certain resistance is called a resistor Common values: – 1-1,000,000Ohm Source: http://en.wikipedia.org/wiki/Resistor PHYS272 - Spring 15 - von Doetinchem - 247 Resistance https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html PHYS272 - Spring 15 - von Doetinchem - 248 Resistance https://phet.colorado.edu/en/simulation/battery-resistor-circuit PHYS272 - Spring 15 - von Doetinchem - 249 Electromotive force and circuits ● ● ● ● ● You need a complete circuit to have a steady current If a charge goes around a complete circuit it will lose potential energy to the ions in the conductor For a steady current a device that is pushing the charge to a higher potential is needed: source of electromotive force (emf) Examples: batteries, generators, solar panels transform, e.g., chemical, mechanical energy into electric energy Ideally: provide constant potential difference, not depending on current PHYS272 - Spring 15 - von Doetinchem - 252 Electromotive force and circuits ● ● Ideal source of emf brings charge to higher potential energy level without increasing the kinetic energy Charge is not used up in a circuit and is not accumulating in the circuit elements. Both sides of the terminal of a battery have the same current for an ideal source of emf. low potential high potential Be careful of charge sign: Electrons would like to go to b (against the electric field) → have to be moved to a to increase the potential energy PHYS272 - Spring 15 - von Doetinchem - 253 Emf in animals: electric eel ● ● Rebuild muscles produce electric potential differences that are combined (in series) to produce strong shocks (500V at ~0.8A) cells pump positive sodium and potassium ions out of the cell via transport proteins http://www.youtube.com/watch?v=1EEy-aXHzRI PHYS272 - Spring 15 - von Doetinchem - 254 Internal resistance ● ● ● ● ● Charges move through the material of a real source of emf feel an internal resistance If the internal resistance behaves like ohmic resistance: For a real source of emf, the terminal voltage equals the emf only if no current is flowing through the source. Current in a circuit drops if the external resistance is getting bigger. Car battery delivers less current when the internal resistance is higher at colder temperatures PHYS272 - Spring 15 - von Doetinchem - 257 Symbols for circuit diagrams ● Conductor with negligible resistance ● Resistor ● Source of emf ● Source of emf with internal resistance ● Voltmeter ● Ammeter PHYS272 - Spring 15 - von Doetinchem - 258 Source in a complete circuit No potential difference between a-a' and b-b' We define the direction electric current as going away from the positive side of our source of emf (although electrons move the other way around) Can be very dangerous PHYS272 - Spring 15 - von Doetinchem - 259 Potential changes around a circuit ● Net change in potential energy for a charge in a complete circuit must be zero → algebraic sum of potential differences around a circuit must be 0 PHYS272 - Spring 15 - von Doetinchem - 260 Energy and power in electric circuits ● ● How fast is energy delivered or extracted? If a charge passes through a circuit element: change of potential energy ● Current stays the same → no gain of kinetic energy ● Power: ● Power for a pure resistance: PHYS272 - Spring 15 - von Doetinchem - 261 Power ● Moving charges collide with atoms in resistor → increase internal energy of material (energy dissipation) ● Maximum power rating of resistors before it overheats ● Power output: I2r ● ● Power input: Direction does not matter for a resistor → energy is dissipated in any case Source with larger emf pushes current backward through source with lower emf (charging of car battery with alternator) PHYS272 - Spring 15 - von Doetinchem - 262 Power 2 2 I r=4A 2=8W I2r ● ● Increasing external resistance reduces power input to resistor Shorted circuit (R=0): – No net power output – dissipates all energy within the source: quickly ruins battery PHYS272 - Spring 15 - von Doetinchem - 263 Tolman-Stewart experiment ● How do we know that the free charges in a metal are negative? – Abruptly stop a rapidly spinning spool of wire and measure the potential difference between the ends of the wire – Simplified version: accelerate a metal rod uniformly – Charges lag behind rod motion → electric field builds up PHYS272 - Spring 15 - von Doetinchem - 264 Tolman-Stewart experiment PHYS272 - Spring 15 - von Doetinchem - 265