Direct-current CircuitsSo far, we have looked at systems with only one resistorquizbuilding blockslight bulbassumptions Iassumptions IIquestionassumptions IIIassumptions IVbasic building blocks: two resistors in seriesresistors in series IIsecond building block: resistors in parallelresistors in parallel IISlide 15question: Christmas tree lightsSlide 17A different Christmas treeKirchhoff’s rulesSlide 20IMPORTANTSlide 22Slide 23Slide 24more than one emfSlide 26circuit breakersQuestion:answerRC circuitsRC circuit IIRC timeSlide 33warningDirect-current CircuitsPHY232 – Spring 2007Jon Pumplinhttp://www.pa.msu.edu/~pumplin/PHY232(Ppt courtesy of Remco Zegers)PHY232 - Remco Zegers - Direct Current Circuits 2Now look at systems with multiple resistors, which are placed in series, parallel or in series and parallel.So far, we have looked at systems with only one resistorfor “ohmic” resistor:PHY232 - Remco Zegers - Direct Current Circuits 3quizAt V=10V someone measures a current of 1A through the below circuit. When she raises the voltage to 25V, the current becomes 2 A. Is the resistor Ohmic? a) YES b) NOPHY232 - Remco Zegers - Direct Current Circuits 4building blocksbattery or other potential source: Provides emf (electromotive force) to the circuitswitch: allows current to flow is closedampere meter: measures currentvolt meter: measures voltageresistorcapacitancelightbulb (I usually show a realistic picture orresistor instead)PHY232 - Remco Zegers - Direct Current Circuits 5light bulbmade of tungsten: =4.8x10-3 1/Ktemperature of filament: ~2800 Kso R=R0[1+(T-T0)]=13R0 !!!consequences: 1) A hot lightbulb has a much higher resistance2) A light bulb usually fails just when switched on because the resistance is small and the current high, and thus the power delivered high (P=I2R)In the demos shown in this lecture, all lightbulbs have the same resistance if at the same temperature, but depending on the current through them, the temperature will be different and thus their resistancesPHY232 - Remco Zegers - Direct Current Circuits 6assumptions I1) The internal resistance of a battery or other voltage source is zero. This is not really true (notice that a battery becomes warm after being used for a while)if this were not the case a system like this:should be replaced withIVIVinternal resistanceVinternal=IRinternalPHY232 - Remco Zegers - Direct Current Circuits 7assumptions IIAn ampere meter (current meter) has a negligible internal resistance, so that the voltage drop over the meter VA=IRA is negligible as wellusually, we do not even draw the ampere meter even though we try to find the current through a certain lineremember that an ampere meter must be placed in series with the device we want to measure the current through1ABPHY232 - Remco Zegers - Direct Current Circuits 8question1ABIf in the above circuit the resistance of the Ampere meteris not zero, it will not measure the right current that would be present if the meter were not present.a) true, the total current will change and thus also the current in the Ampere meterb) not true, current cannot get stuck in the line and thus the measurement will not be affected10VPHY232 - Remco Zegers - Direct Current Circuits 9assumptions IIIa volt meter has an infinite internal resistance, so that no current will flow through it.usually, we do not even draw the volt meter even though we try the potential over a certain branch in the circuitremember that a volt meter must be placed in parallel with the device we want to measure the voltage over1A BPHY232 - Remco Zegers - Direct Current Circuits 10assumptions IVWe can neglect the resistance of wires that connect the various devices in our circuit. This is true as long as the resistance of the device is much larger than that of the wiresPHY232 - Remco Zegers - Direct Current Circuits 11basic building blocks: two resistors in seriesThe water flow (m3/s) through the two narrow pipes must be equal (else water gets stuck), so the pressure drop is larger over the narrowest of the two. The total pressure drop is equal to the sum of the two pressure drops over both narrow pipesThe current (I) through the two resistors must be equal (else electrons would get stuck), so the voltage drop is larger over the highest of the two. The total voltage drop is equal to the sum of the two voltage drops over the resistors. 2m wide1m widePoiseuille:Flow~Pr4/lPHY232 - Remco Zegers - Direct Current Circuits 12The voltage over R1 and R2:1)if we want to replace R1,R2 with oneequivalent R:2)and by combining 1) and 2)resistors in series IIFor n resistors placed in series in a circuit:Req = R1+R2+…+RnNote: Req>Ri I=1,2…n the equivalent R is always larger than each of the separate resistorsIR1R2Vdemo2 light in seriesPHY232 - Remco Zegers - Direct Current Circuits 13second building block: resistors in parallelThe pressure drop over the two narrow pipes must be equal (before and after the pipes the pressure is the same), but the water prefers to flow through the wider canal, i.e, the flow (m3/s) is higher through the wider canal.The voltage drop over the two resistors must be equal (before and after the resistors the voltage is the same), but the electrons prefer to go through the smaller resistor, i.e, the current (A) is higher through the smaller resistor.1m wide1.5m widePHY232 - Remco Zegers - Direct Current Circuits 14For the current through the circuit:1)if we want to replace R1,R2 with oneequivalent R:2)and by combining 1) and 2):resistors in parallel IIFor n resistors placed in parallel in a circuit:1/Req = 1/R1+1/R2+…+1/RnNote: Req<Ri with I=1,2…n Req is always smaller than each of the separate resistorsI2R1R2VI1Idemo2 light in parallelPHY232 - Remco Zegers - Direct Current Circuits 15questionwhat is the equivalent resistance of all resistors as placed in the below circuit? If V=12V, what is the current I?IR1R2VR3R1=3 OhmR2=3 OhmR3=3 OhmV=12VR2 & R3 are in parallel1/R23=1/R2+1/R3=1/3+1/3=2/3R23=3/2 OhmR1 is in series with R23R123=R1+R23=3+3/2=9/2 OhmI=V/R=12/(9/2)=24/9=8/3 APHY232 - Remco Zegers - Direct Current Circuits 16question: Christmas tree lightsA tree is decorated with a string of many equal lights placed in parallel. If one burns out (no current flow through it), what happens to the others? a) They all stop shiningb) the others get a bit dimmerc) the others get a bit brighterd) the brightness of the