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Ohm’s Law Physics 102 Professor Lee Carkner Lecture 14 PAL #13 Capacitors What is capacitance? Q= CV C = Q/V = 0.005/1000 = Jury-rig a replacement out of metal foil and Teflon coating (k = 2.1, thickness = 0.01 mm). C = ke0A/d A = Cd/ke0 = (5X10-6)(0.00001)/(2.1)(8.85X10-12) A = How can such a device be portable? Circuit Theory We have already discussed potential difference This charge motion is called the current (symbol: I) Energy can be extracted from the current due to resistance (symbol: R) Current I = DQ/Dt The units are amperes (amps) or coulombs per second The most common charge carrier is the electron Inside a Wire The wire is full of electrons However, the electrons do not move in a straight line Electrons do not move freely, directly or rapidly Drift Speed We can find the drift speed in terms of the properties of the wire: Where I is the current, n is the electron density, q is the charge on the electron and A is the cross sectional area of the wire Electron Motion Current Conundrums The drift speed is very small (~mm per second), yet the effect of current is felt instantaneously Electrons move randomly, yet current flows in only one direction The direction of the current is opposite the motion of the electrons Resistivity Why? The materials resist the flow of current Good conductors have low resistivity, good insulators have high resitivities Resistivity is a property of a particular type of material rather than of a particular wire Resistance Short, wide wires have less resistance than long, narrow wires The resistance can be written as: R = r (L/A) The units of resistance are ohms (volts per ampere) Ohm’s Law How much current do you get if you put a potential difference V across a wire with resistance R? High voltage, low resistance means large current Commonly written as: V = IR However, the law only holds for certain types of materials (called ohmic) Simple Circuit Using Ohm’s Law Ohm’s law quantifies the way circuits work Can write in different ways: The voltage varies directly with resistance when current is constant High voltage and low resistance means high current Today’s PAL A 1.5 volt battery produces 167 A of current when connected to a 1 meter long, 2 mm thick wire. What is the wire made of? Discuss the validity of the following claim: “The relationship R = V/I tells us that the resistance of a wire is directly proportional to the potential difference applied to it.” Temperature and Resistance Resistors convert energy from the current into heat Temperature also affects electronic properties This increased random motion means collisions are more frequent and it is harder for current to flow Resistance generally increases with temperature Superconductivity If we set up a current in a wire and then take away the battery the current fades to zero If the resistance was zero the current would keep flowing even without a battery Such materials are called superconductors Superconductors have R go to zero as T gets small Energy in Electric Circuits As the charges flow (as current) they convert the potential energy to kinetic energy We should be able to relate the potential difference, current and resistance to the energy produced Energy Dispersion Rate The energy per electron is DPE = qDV so energy per coulomb is DV (Energy/Coulomb)(Coulomb/Second) = (Energy/Second) IDV = P Power Using Ohm’s law (DV = IR) we can write: In general we will know the values of R (since it depends on the properties of the resistor) and DV (since we should know the voltage of our source or battery) Lightbulbs A common circuit element is the lightbulb Household lightbulbs are rated in watts In the US, most power outlets produce 120 volts of potential difference Those that do not use a transformer Coronal Loop on the Sun Joule Heating This is how an electrical resistance heater works Joule heating is seen in the natural world: Can produce energy in the Earth’s atmosphere Next Time Read: 19.1-19.4, 18.6, 19.7 Homework: Ch 18, P 35, (+one not in book), Ch 19, P 5, 9