no tagsLecture 017: Electric Circuits - Resistors and BatteriesSteveSekula, 4 October 2010 (created 3 October 2010)General Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...1 of 7 10/04/2010 08:13 AMGoals of this lectureDevelop the mathematics to describe what we saw last timeIntroduce the language of circuitsReview from last timeWe hooked up lightbulbs - resistors - in parallel and series to a 110Velectric potential difference. We made a few observations:resistors (lightbulbs) in parallel achieve their full power (same voltage,different currents)resistors in series don't achieve their full power (different voltages,same current).Today we can develop the language to describe what we saw.Series and Parallel ResistorsIntroduce the symbol for the resistor and use this to discuss a basiccircuit diagramLines represent very, very good conductors (assumed to be perfect)jagged squiggles describes resistors - conductors whose resistivityand geometry inhibit the flow of electronsfor a bit longer, we'll denote the source of electric potentialdifference as a gap with a "V" inside the gap.We considered series and parallel capacitors. Series and parallel are thetwo simplest way to connect ANY two electronic components. Twocomponents are in series if the current has nowhere to go but throughboth components. They are in parallel if the current can flow eitherthrough one or the other component.Let's consider series and parallel resistors.General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...2 of 7 10/04/2010 08:13 AMSeries ResistorsWhen in series, and if the circuit is in a steady state - that is, there is nocharge buildup anywhere in the circuit - then the current has no choicebut to go through one resistor, , and then the other, .The current through series resistors is the same in both resistorsWe can write Ohm's Law for each resistor:We know that . We also know that the total electric potential inthe circuit is , and that the sum of the individual potential differencesmust add up to that:Finally, we know that whatever the TOTAL resistance of the circuit, thereis also an Ohm's Law for that:We can then solve for the total resistance:Thus we can make the identification that:The total resistance of series resistors is the sum of the individualR 1R 2V R 1= I1 1V R 2= I2 2I 1= I2= ItotalV totalV total= V1+ V2V R total= Itotal totalV (R ) R total= V1+ V2= Itotal1+ R2= Itotal totalR : total= R1+ R2General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...3 of 7 10/04/2010 08:13 AMresistances.We can then reverse this and use Ohm's Law to solve for the voltage acrosseach resistor:V VV VAdd these up and you will recover the total voltage, .Ideal and Real BatteriesLet's take a moment to talk about batteries. We've been using an unnamed"source of electric potential difference, " to attack these problems. Anideal battery delivers a steady voltage across its terminals, regardless ofthe current through the circuit. We denote the ability of a battery to createan electric field and do work on charge as its electromotive force, or EMF.We write the work per unit charge that the battery can do as .Let's revisit series resistor results in lieu of this change in notation, nowthat we're introducing real batteries:The battery voltage divides between the two resistors, based on theirresistance. That is also why a combination of series resistors is called avoltage dividerIf you need to take a large source of EMF and subdivide its voltage into1=R1R1+ R2total2=R2R1+ R2totalV totalV E V E 1=R1R1+ R2V E 2=R2R1+ R2General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...4 of 7 10/04/2010 08:13 AMsmaller pieces to work on more delicate equipment, you need to useseries resistors to create a voltage divider.Consider the kindle. In your homework, you determined that thevoltage required to move E-Ink particles is really tiny - about0.2mV. Why can I plug my kindle into the wall and not be afraid ofthe high voltage - 110V - frying my electronics? I'm protected by atleast one voltage divider built into the circuitry, tamping down thewall voltage to something more reasonable for this device.Let's think about real batteries for a second.What differentiates AAA, AA, and D-type 1.2V batteries? They all deliver1.2V of potential difference, so why the differentiation? (Is this just aconspiracy to force me to buy different batteries for all my toys?!)Use this discussion to motivate the discovery that different battery typescan deliver different currents in the same period. D-type batteries candeliver about 3A for an hour, AA-type batteries 2.5A for an hour, andAAA-type batteries about 1A for an hour. That must mean that theirinternal RESISTANCES are different. According to the Energizercompany's own data, AA-type batteries have an internal resistance of about.http://data.energizer.com/PDFs/BatteryIR.pdfSo batteries are sources of electric potential difference AND resistance.The chemical reactions that allow them to create an EMF are not steadyover time (batteries wear down, and batteries can't behave perfectly for allcurrents). In effect, a battery is a source of EMF in series with a resistor,creating an internal voltage divider. The terminal voltage is always a bitless than the rated voltage for the battery. If the resistive load in theexternal circuit, , is big compared to the internal battery resistance,, then the voltage delivered by the battery is nearly :Even if we short-circuit the battery (connect its terminals - ALWAYS A BAD0:2Ê R LR intE V E < battery=RLRint+ RL! Rint< RL! EGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...5 of 7 10/04/2010 08:13 AMIDEA!), we don't get infinite current because of that internal resistance. Infact, the most current we ever get isFor a AA-type battery, that gives us:How much power is that? Will that be bad?Unknown control sequence '\W'That's enough to raise the temperature of your hand, in contact with thebattery, by 1-2 degrees celcius each second. That would be noticeably hotin a very short period of time, and it's not at all good for the battery.Parallel ResistorsWhat about resistors in parallel? Now, the current across the two resistorsis not the same, but the
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