PHY2049: Chapter 271Chapter 27 SubjectsÎEmf devices (review)ÎResistors in series and parallelÎPower (examples)ÎMultiloop circuitsÎAmmeters and voltmetersÎRC circuits and time constantPHY2049: Chapter 272Emf devicesÎWhat do they do?Maintain potential difference by pumping charge, which requires work. (Total charge remains 0.)ΓCharge up” a batteryDon’t be misled by this expressionPHY2049: Chapter 273ÎOnly one battery in the circuitÎTwo batteries in seriesÎBatteries in parallelSimple Circuitsℇℇ = VVℇ1VℇVℇ2ℇ1+ ℇ2 = VTo be useful and safe, their ℇ must be the same.PHY2049: Chapter 274Resistors in SeriesÎLike additional constriction. It becomes harder for current to flow.ÎMeasure of difficulty for current to flow: RÎThus21RRReq+=R1R2Req= equivalent resistanceReq(in general)(Read Section 27-5 for rigorous derivation)⋅⋅⋅+++=321RRRReqℇℇPHY2049: Chapter 275Resistors in ParallelÎAdds a bypass. It becomes easier for current to flow. ÎMeasure of easiness for current flow: 1/R (‘conductance’)ÎTherefore,ÎReqis smaller than the smallest21111RRReq+=R1R2ℇReq= equivalent resistanceℇReqL+++=3211111RRRReq(in general)(Read Section 27-7 for rigorous derivation)PHY2049: Chapter 276ÎAs more resistors R are added in parallel to the circuit, how does total resistance between points P and Q change?(a) increases(b) remains the same(c) decreasesÎIf the voltage between P & Q isheld constant, and more resistorsare added, what happens tothe current through each resistor?(a) increases(b) remains the same(c) decreasesResistors in ParallelOverall current increases,but current through eachbranch is still V/R.PHY2049: Chapter 277Resistors in Parallel (continued)21111RRReq+=R1R2ℇℇReq(Engineers and physicists memorize this formula.)2121RRRRReq+=PHY2049: Chapter 278Parallel-Series ComboÎWhat is the net resistance of the circuit connected to the battery? Each resistance has R = 3 kΩ1&2 in series ⇒ 6kΩ3 in parallel with 1&2 ⇒ 2kΩ4 in series ⇒ 5kΩ5 in parallel ⇒ 15/8 kΩ = 1.875 kΩ6 in series ⇒ 4.875 kΩ2121RRRRReq+=12345621111RRReq+=2121RRRRReq+=is faster thanPHY2049: Chapter 279CurrentsÎIf the light bulbs are all the same in each of these two circuits, which circuit has the higher current?(a) circuit A(b) circuit B(c) both the sameÎIn which case is each light bulbbrighter?(a) circuit A(b) circuit B(c) both the sameABCurrent through eachbranch is unchanged (V/R)PHY2049: Chapter 2710CurrentsÎCurrent flows through a light bulb. If a wire is now connected across the bulb as shown, what happens?(a) All the current continues to flow through the bulb(b) Current splits 50-50 into wire and bulb(c) All the current flows through the wire(d) None of the aboveThe wire “shunt” has almost no resistance and it is in parallel with a bulb having resistance.Therefore all the current follows the zero (or extremely low) resistance path.PHY2049: Chapter 2711CurrentsÎThe light bulbs in the circuits below are identical. Which configuration produces more light?(a) circuit I(b) circuit II(c) both the sameCircuit II has ½ current of each branch of circuit I, so each bulb is ¼ as bright.The total light in circuit I is thus 4x that of circuit II.PHY2049: Chapter 2712ÎTwo light bulbs A and B are connected in series to a constant emf source. When a wire is connected across B, what will happen to bulb A?(a) burns more brightly than before(b) burns as brightly as before(c) burns more dimly than before(d) goes outCurrentsThe wire shunt effectively eliminates thesecond resistance, hence increasing thecurrent in the circuit by 2x. The firstbulb burns 4x brighter (I2 R).PHY2049: Chapter 2713CurrentsÎThe three light bulbs in the circuit are identical. The current flowing through bulb B, compared to the current flowing through bulb A, is(a) 4 times as much(b) twice as much(c) the same(d) half as much(e) 1/4 as muchBranch of circuit A has ½ resistance, thus it has 2x current.PHY2049: Chapter 2714Household CircuitsÎAll devices are added in parallel.Why?ÎOverload: too many devices that require a lot of current can draw more current than wires can handle.Overheating of wiresFire hazard!PHY2049: Chapter 2715PowerÎThe three light bulbs in the circuit are identical. What is the brightness of bulb B compared to bulb A?(a) 4 times as much(b) twice as much(c) the same(d) half as much(e) 1/4 as muchUse P = I2R. Thus 2x current in A means it is 4x brighter.Use P = IV. 2x current and voltage. Same conclusion.PHY2049: Chapter 2716Power (Problem solving) ÎFind the value of R that maximizes power emitted by R. I12ΩI1I218VR6Ω121218 12124612TRRRRIRRR=++==+++222PIR=122111212 1212 4RTRIIIRR==⇒=++ +()22221444RPIRR==+Maximize249WRP=Ω=Find I2or V2Very large R. Very small R.PHY2049: Chapter 2717Power lines ÎAt large distances, the resistance of power lines becomes significant. To transmit maximum power, is it better to transmit high V, low I or high I, low V?(a) high V, low I(b) low V, high I(c) makes no differenceÎWhy do birds sitting on a high-voltage power line survive?They are not touching high and low potential simultaneously to form a circuit that can conduct currentPower loss is I2R, so wantto minimize current.PHY2049: Chapter 2718Concept QuestionsÎ Two incandescent light bulbs—40 W and 100 W. Which has a smaller resistance?Î 40 W light bulb made for US market. If used in Argentina, will it be brighter, dimmer, or no different?Î Connect a piece of copper wire to a (constant) current source. What will happen?Î Connect it to an emf source (battery or power outlet). What will happen?PHY2049: Chapter 2719CircuitsÎWhen the switch S is closed, then:What happens to the voltage across each resistor?What happens to the current through each resistor?What happens to the total power output of the battery?Let R1= R2= R3= R4= 90 Ω and V = 9 V. Find the current through each resistor before and after closing the switch.Before¾I1= 9/135 = 1/15 A¾I2= 0¾I3= I4=I1/2=1/30 AAfter¾I1= 9/120 = 3/40 A¾I2= I3= I4= 1/40 APHY2049: Chapter 2720Circuit Problem (1)ÎThe light bulbs in the circuit are identical. What happens when the switch is closed?(a) both bulbs go out(b) the intensity of both bulbs increases(c) the intensity of both bulbs decreases(d) nothing
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