MasteringPhysics: Assignment Print View Http . - Chris's Pencasts

MasteringPhysics: Assignment Print View1 of ntPrint?assignmentID .Chapter 32 HomeworkDue: 8:00am on Tuesday, March 30, 2010Note: To understand how points are awarded, read your instructor's Grading Policy.[Return to Standard Assignment View]Comparing brightness of light bulbsConsider five identical light bulbs (A - E) connected to a battery as shown in the circuit below.Part ARank the brightness of all five bulbs from brightess to dimmest.Hint A.1BrightnessThe brightness of a light bulb is related to the powerdissipated by that bulb. Recall that power depends upon the square of the currentthat passes through the bulb and the resistanceof the bulb. Since eachlight bulb in this circuit has the same resistance, the lightbulb with the largest current passing through it will be the brightest.Hint A.2Compare the brightness of bulbs A and BHint not displayedHint A.3Compare the brightness of bulbs D and EHint not displayedHint A.4Compare the brightness of bulbs C and DHint not displayedHint A.5Compare the brightness of bulbs C and AHint not displayedHint A.6Compare the brightness of bulbs D and AHint not displayedRank the bulbs from brightest to dimmest. To rank items as equivalent, overlap them.ANSWER:ViewCorrectHow does this change effect the circuit?Suppose bulb E is unscrewed and removed from its socket. (The empty socket remains in the circuit.)Part BDoes bulb A get brighter, dimmer, or stay the same brightness?Hint B.1How to approach the problemHint not displayedHint B.2Determine how the current changesHint not displayedANSWER:Light bulb A gets brighter.Light bulb A gets dimmer.Light bulb A stays the same brightness.CorrectConceptual Question 32.8Part ARank in order, from largest to smallest, the powerstodissipated by the four resistors in the figure.Rank from largest to smallest. To rank items as equivalent, overlap them.3/30/2010 2:18 PM

MasteringPhysics: Assignment Print View2 of ntPrint?assignmentID .ANSWER:ViewCorrectProblem 32.8Part AHow much power is dissipated by the 12resistor in the figure ?Express your answer using two significant figures.ANSWER: 1.9CorrectPart BHow much power is dissipated by the 18resistor in the figure?Express your answer using two significant figures.ANSWER: 2.9CorrectSeries And Parallel ConnectionsLearning Goal: To learn to calculate the equivalent resistance of the circuits combining series and parallel connections.Resistors are often connected to each other in electric circuits. Finding the equivalent resistance of combinations of resistors is a common and important task. Equivalent resistance is defined as the single resistance thatcan replace the given combination of resistors in such a manner that the currents in the rest of the circuit do not change.Finding the equivalent resistance is relatively straighforward if the circuit contains only series and parallel connections of resistors.An example of a series connection is shown in the diagram:For such a connection, the current is the same for all individual resistors and the total voltage is the sum of the voltages across the individual resistors.Using Ohm's law (), one can show that, for a series connection, the equivalent resistance is the sum of the individual resistances.Mathematically, these relationships can be written as:An example of a parallel connection is shown in the diagram:For resistors connected in parallel the voltage is the same for all individual resistors becausethey are all connected to the same two points (A and B on the diagram). The total current is thesum of the currents through the individual resistors. This should makes sense as the total current"splits" at points A and B.Using Ohm's law, one can show that, for a parallel connection, the reciprocal of the equivalentresistance is the sum of the reciprocals of the individual resistances.Mathematically, these relationships can be written as:NOTE: If you have already studied capacitors and the rules for finding the equivalent capacitance, you should notice that the rules for the capacitors are similar - but not quite the same as the ones discussed here.In this problem, you will use the the equivalent resistance formulas to determinefor various combinations of resistors.3/30/2010 2:18 PM

MasteringPhysics: Assignment Print View3 of ntPrint?assignmentID .Part AFor the combination of resistors shown, find the equivalent resistance between points A and B.Express your answer in Ohms.ANSWER: 9CorrectThese resistors are connected in series; the current through each is the same.Part BFor the set-up shown, find the equivalent resistance between points A and B.Express your answer in Ohms.ANSWER: 2CorrectThis is a parallel connection since the voltage across each resistor is the same.Part CFor the combination of resistors shown, find the equivalent resistance between points A and B.Hint C.1How to approach the questionHint not displayedHint C.2What kind of connection is this?Hint not displayedExpress your answer in Ohms.ANSWER: 5CorrectIn this case, you cannot say that all three resistors are connected either in series or in parallel. You have a combination of a series and a parallel connection.Some circuits may contain a large number of resistors connected in various ways. To determine the equivalent resistance of such circuits, you have to take several steps, carefully selecting the "sub-combinations"of resistors connected in relatively obvious ways. Good record-keeping is essential here.The next question helps you practice this skill.Part DFor the combination of resistors shown, find the equivalent resistance between points A and B.3/30/2010 2:18 PM

MasteringPhysics: Assignment Print View4 of 8Hint mentPrint?assignmentID .How to approach the questionHint not displayedHint D.2Findfor the "4-6-12" combinationHint not displayedHint D.3Findfor the top branchHint not displayedHint D.4Findfor the bottom branchHint not displayedExpress your answer in Ohms.ANSWER: 3CorrectThe next level of analyzing a circuit is to determine the voltages across and the currents through the various branches of the circuit. You will practice that skill in the future.Of course, there are circuits that cannot possibly be represented as combinations of series and parallel connections. However, there are ways to analyze those, too.Problem 32.4Part AWhat is the magnitude of the current in the 30ANSWER:resistor in the figure ? 0.100CorrectPart BWhat is the direction of the current in the 30ANSWER:resistor in the figure?from right to left through the resistorfrom left to right through the resistor.CorrectKirchhoff's Rules and Applying ThemLearning Goal: To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem.This problem introduces Kirchhoff's two rules for circuits:Kirchhoff's loop rule: The sum of the voltage changes across the circuit elements forming any closed loop is zero.Kirchhoff's junction rule: The algebraic sum of the currents into (or out of) any junction in the circuit is zero.The figure shows a circuit that illustrates the concept of loops, which are colored red and labeled loop 1 and loop 2. Loop 1 is the loop around the entirecircuit, whereas loop 2 is the smaller loop on the right. To apply the loop rule you would add the voltage changes of all circuit elements around the chosenloop. The figure contains two junctions (where three or more wires meet)--they are at the ends of the resistor labeled. The battery supplies a constantvoltage, and the resistors are labeled with their resistances. The ammeters are ideal meters that readandrespectively.The direction of each loop and the direction of each current arrow that you draw on your own circuits are arbitrary. Just assign voltage drops consistently andsum both voltage drops and currents algebraically and you will get correct equations. If the actual current is in the opposite direction from your current arrow,your answer for that current will be negative. The direction of any loop is even less imporant: The equation obtained from a counterclockwise loop is thesame as that from a clockwise loop except for a negative sign in front of every term (i.e., an inconsequential change in overall sign of the equation because itequals zero).3/30/2010 2:18 PM

MasteringPhysics: Assignment Print View5 of ntPrint?assignmentID .Part AThe junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that are in a steady state.Hint A.1At the junctionHint not t BApply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistanceHint B.1).Elements in seriesHint not displayedAnswer in terms of given quantities, together with the meter readingsandand the current.ANSWER:CorrectIf you apply the juncion rule to the junction above, you should find that the ezpression you get is equivalent to what you just obtained for the junction labeled 1. Obviously the conservation of charge or currentflow enforces the same relationship among the currents when they separate as when they recombine.Part CApply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow. Remember that the current meter is ideal.Hint C.1Elements in series have same currentHint not displayedHint C.2Sign of voltage across resistorsHint not displayedHint C.3Voltage drop across ammeterHint not displayedExpress the voltage drops in terms of,,, the given resistances, and any other given quantities.ANSWER:CorrectPart DNow apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.Express the voltage drops in terms of,,, the given resistances, and any other given quantities.ANSWER:CorrectThere is one more loop in this circuit, the inner loop through the battery, both ammeters, and resistorsand. If you apply Kirchhoff's loop rule to this additional loop, you will generate an extra equation thatis redundant with the other two. In general, you can get enough equations to solve a circuit by either1. selecting all of the internal loops (loops with no circuit elements inside the loop) or2. using a number of loops (not necessarily internal) equal to the number of internal loops, with the extra proviso that at least one loop pass through each circuit element.Problem 32.47Part AWhat is the resistanceANSWER:in the figure ?20.0Correct3/30/2010 2:18 PM

MasteringPhysics: Assignment Print View6 of ntPrint?assignmentID .Part BWhat is the emf of the battery in the figure?ANSWER:60.0CorrectProblem 32.65Part AWhat is the current through the 10resistor in the figure?Express your answer using two significant figures.ANSWER: 0.12CorrectPart BIs the current from left to right or right to left?ANSWER:left to rightright to leftCorrectRC Circuit and Current Conceptual QuestionIn the diagram below,the two resistors,and, are identical and the capacitor is initially uncharged with the switch open.Part AHow does the current throughHint A.1compare with the current throughimmediately after the switch is first closed?Using Kirchhoff's junction rule for currentsHint not displayedANSWER:The current throughthe current through.CorrectPart BHow does the current throughHint B.1compare with the current througha very long time after the switch has been closed?Using Kirchhoff's junction rule for currentsHint not displayedHint B.2Current associated with a fully charged capacitorHint not displayedANSWER:The current throughthe current through.CorrectPart C3/30/2010 2:18 PM