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# Week 2 Short Assignments 1220

Mizzou

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This 15 page Bundle was uploaded by Dragon Note on Thursday March 24, 2016. The Bundle belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 191 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.

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Date Created: 03/24/16

Short Assignment By 2/3/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/3/2016 Due: 11:00am on Wednesday, February 3, 2016 To understand how points are awarded, read therading Policy for this assignment. A Stretchable Resistor A wire of length and cross-sectional area has resistance . Part A What will be the resistance of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched. Express your answer in terms of the wire's original resistance . Hint 1. Formula for the resistance of a wire The resistance of a wire with resistivity , length , and cross-sectional area is given by . Which of the quantities on the right-hand side of the equation change when the wire is stretched? Hint 2. Find the cross-sectional area of the stretched wire Let be the new cross-sectional area of the wire. The density of the wire is unchanged upon stretching. Also, the mass of the wire cannot have changed upon stretching. Therefore, the new volume of the wire must be the same as the old volume. Use the above information and the fact that the stretched length of the wire is to find . Express your answer in terms of . Hint 1. Formula for the volume of a cylinder The wire can be treated as a cylinder. The volume of this cylinder is given by = Old Area Old length = New Area New length ANSWER: = ANSWER: = Correct Short Assignment By 2/3/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Problem 21.20 When a potential difference of 12 is applied to a wire 7.2 long and 0.34 in diameter the result is an electric current of 2.2 . Part A What is the resistivity of the wire? Express your answer using two significant figures. ANSWER: = 6.9×10 −8 Correct Score Summary: Your score on this assignment is 100%. You received 1.5 out of a possible total of 1.5 points. Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/5/2016 Due: 11:00am on Friday, February 5, 2016 To understand how points are awarded, read therading Policy for this assignment. Series And Parallel Connections Learning 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 that can 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 because they are all connected to the same two points (A and B on the diagram). The total current is the sum 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 equivalent resistance is the sum of the reciprocals of the individual resistances. Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... 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 determinfor various combinations of resistors. Part A For the combination of resistors shown, find the equivalent resistance between points A and B. Express your answer in Ohms. ANSWER: = 9 Correct These resistors are connected in series; the current through each is the same. Part B For the set-up shown, find the equivalent resistance between points A and B. Express your answer in Ohms. Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: = 2 Correct This is a parallel connection since the voltage across each resistor is the same. Part C For the combination of resistors shown, find the equivalent resistance between points A and B. Express your answer in Ohms. Hint 1. How to approach the question You cannot say that all three resistors are connected either in series or in parallel: this circuit has to be viewed as a combination of different connections. Find the equivalent resistance of the "4-Ohm-12 Ohm" combination first. Hint 2. What kind of connection is this? The 2-Ohm resistor is connected: ANSWER: Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... in series with the 4-Ohm resistor in series with the 12-Ohm resistor in series with the combination of the 4-Ohm and the 12-Ohm resistors in parallel with the 4-Ohm resistor in parallel with the 12-Ohm resistor in parallel with the combination of the 4-Ohm and the 12-Ohm resistors ANSWER: = 5 Correct In 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 D For the combination of resistors shown, find the equivalent resistance between points A and B. Express your answer in Ohms. Hint 1. How to approach the question Find separately the equivalent resistances of the top and the bottom branches of the circuit; then combine them. Hint 2. Find for the "4-6-12" combination Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... What is the equivalent resistance for the "4 ohm - 6 ohm - 12 Ohm" combination? Express your answer in ohms. ANSWER: = 2 Hint 3. Find for the top branch What is the equivalent resistance for the top branch of the circuit (between C and D)? Express your answer in ohms. ANSWER: = 6 Hint 4. Find for the bottom branch What is the equivalent resistance for the bottom branch of the circuit (between E and F)? Express your answer in ohms. ANSWER: = 6 ANSWER: = 3 Correct The 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. Power Dissipation in Resistive Circuit Conceptual Question A single resistor is wired to a battery as shown in the diagram below. Define the total power dissipated by th.s circuit as Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Now, a second identical resistor is wired in series with the first resistor as shown in the second diagram to the left . Part A What is the power, in terms of , dissipated by this circuit? Express your answer in terms of . Hint 1. How to find the power dissipated by a circuit The power dissipated by a circuit (or by an element in a circuit) is defined by the relation . If the circuit consists of resistors, we can combine this relation with Ohm's law, , to yield two alternate versions of the power formula: and . Because several circuit parameters can be changing simultaneously, it is easiest to use the formula in which only one of the terms is changing for your situation. This makes it much easier to determine the power dissipated in a resistive circuit. Hint 2. Effect of adding a resistor in series Adding a resistor in series affects both the total resistance and total current in a circuit. Combining an understanding of these changes with the appropriate version of the power formula should allow you to answer this question. Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: Correct The second resistor is now removed from the circuit and rewired in parallel with the original resistor as shown in the schematic to the left Part B What is the power, in terms of , dissipated by this circuit? Express your answer in terms of . Hint 1. How to find the power dissipated by a circuit The power dissipated by a circuit (or by an element in a circuit) is defined by the relation . If the circuit consists of resistors, we can combine this relation with Ohm's law, , to yield two alternate versions of the power formula: and . Because several circuit parameters can be changing simultaneously, it is easiest to use the formula in which only one of the terms is changing for your situation. This makes it much easier to determine the power dissipated in a resistive circuit. Hint 2. Effect of adding a resistor in parallel Adding a resistor in parallel affects both the total resistance and current in a circuit. Combining an understanding of these changes with the appropriate version of the power formula should allow you to answer this question. ANSWER: Short Assignment By 2/5/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Score Summary: Your score on this assignment is 100%. You received 3 out of a possible total of 3 points. Short Assignment by 2/1/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment by 2/1/2016 Due: 11:00am on Monday, February 1, 2016 To understand how points are awarded, read therading Policy for this assignment. Capacitance: A Review Learning Goal: To review the meaning of capacitance and ways of changing the capacitance of a parallel-plate capacitor. Capacitance is one of the central concepts in electrostatics. Understanding its meaning and the difference between its definition and the ways of calculating capacitance can be challenging at first. This tutorial is meant to help you become more comfortable with capacitance. Recall the fundamental formula for capacitance: , where is the capacitance in farads, is the charge stored on the plates in coulombs, and is the potential difference (or voltage) between the plates. In the following problems it may help to keep in mind that the voltage is related to the strength of the electric field and the distance between the plates, , by . Part A What property of objects is best measured by their capacitance? ANSWER: the ability to conduct electric current the ability to distort an external electrostatic field the ability to store charge Correct Capacitance is a measure of the ability of a system of two conductors to store electric charge and energy. It is defined as . This ratio remains constant as long as the system retains its geometry and the amount of dielectric does not change. Capacitors are special devices designed to combine a large capacitance with a small size. However, any pair of conductors separated by a dielectric (or vacuum) has some capacitance. Even an isolated electrode has a small capacitance. That is, if a charge is placed on it, its potential with respect to ground would change, and the ratio is its capacitance . Part B Consider an air-filled charged capacitor. How can its capacitance be increased? Hint 1. What does capacitance depend on? Capacitance depends on the inherent properties of the system of conductors, such as its geometry and the presence of dielectric, not on the charge placed on the conductors. Specifically, capacitance depends on the area of the conducting plates and the distance between the plates and is given by , where is a constant called the permittivity of free space. Short Assignment by 2/1/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: Increase the charge on the capacitor. Decrease the charge on the capacitor. Increase the spacing between the plates of the capacitor. Decrease the spacing between the plates of the capacitor. Increase the length of the wires leading to the capacitor plates. Correct Part C Consider a charged parallel-plate capacitor. How can its capacitance be halved? Check all that apply. ANSWER: Double the charge. Double the plate area. Double the plate separation. Halve the charge. Halve the plate area. Halve the plate separation. Correct Part D Consider a charged parallel-plate capacitor. Which combination of changes would quadruple its capacitance? ANSWER: Double the charge and double the plate area. Double the charge and double the plate separation. Halve the charge and double the plate separation. Halve the charge and double the plate area. Halve the plate separation and double the plate area. Double the plate separation and halve the plate area. Correct Short Assignment by 2/1/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Parallel-Plate Capacitors with Different Surface Areas Suppose two parallel-plate capacitors have the same charge , but the area of capacitor 1 is and the area of capacitor 2 is . Part A If the spacing between the plates, , is the same in both capacitors, and the voltage across capacitor 1 is , what is the voltage across capacitor 2? Hint 1. How to approach the problem The voltage between the plates of a capacitor is proportional to the charge accumulated on the plates. The proportionality constant in this relation depends on the geometry of the capacitor. Therefore, it will be different for capacitors 1 and 2. To solve this problem you can use proportional reasoning to find this relation between voltage and charge . Find the simplest equation that contains these variables and other known quantities from the problem. Write this equation twice, once to describe capacitor 1 and again to relate the same quantities for capacitor 2. You need to write each equation so that all the constants are on one side and your variables are on the other. Since your variable is in this problem, you want to write your equations in the form . To finish the problem you need compare the two cases presented in the problem. For this question you should find the ratio of the voltage in capacitor 2, , to that in capacitor 1, : . Hint 2. Find an expression for the voltage between the plates Which of the following expressions gives the magnitude of the voltage between the plates of a capacitor of capacitance ? In the expressions below, is the magnitude of the charge accumulated on either plate of the capacitor. ANSWER: Hint 3. Capacitance of a parallel-plate capacitor The capacitance of a parallel-plate capacitor in vacuum is directly proportional to the area of each plate and inversely proportional to the separation between the plates: , where is a the permittivity of free space expressed in . ANSWER: Short Assignment by 2/1/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Even though the spacing between the plates is the same in both capacitors, the capacitor with the larger plates has a lower voltage between its plates. In fact, because the capacitors are equally charged, capacitor 2 has a smaller surface charge density, and therefore a weaker electric field between its plates. Since the voltage between two parallel plates is proportional to the electric field, capacitor 2 also has a lower voltage. Part B If the spacing between the plates in capacitor 1 is , what should the spacing between the plates in capacitor 2 be to make the capacitance of the two capacitors equal? Hint 1. How to approach the problem The capacitance of a capacitor depends on the geometry of the capacitor. In particular, for a parallel-plate capacitor, there exists a simple relation among the capacitance , the surface area of the plates, and the separation between the plates. To solve this problem you can use proportional reasoning to find this relation. Find the simplest equation that contains these variables and other known quantities from the problem. Write this equation twice, once to describe capacitor 1 and again to relate the same quantities for capacitor 2. You need to write each equation so that all the constants are on one side and your variables are on the other. Since your variable is in this problem, you want to write your equations in the form . To finish the problem you need compare the two cases presented in the problem. For this question you should find the ratio of the spacing between the plates in capacitor 2, , to that in capacitor 1, : . Hint 2. Find an expression for the spacing between the plates of a capacitor Given a parallel-plate capacitor of capacitance and surface area , which of the following expressions gives the separation between the plates? In the equations below, is a constant expressed in . ANSWER: ANSWER: Short Assignment by 2/1/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Since the capacitance of a capacitor depends only on the geometry of the capacitor, capacitors 1 and 2 have the same capacitance only when the spacing between the plates in capacitor 2 is twice that in capacitor 1. This balances the effect of the different areas of the two capacitors. Score Summary: Your score on this assignment is 100%. You received 1.5 out of a possible total of 1.5 points.

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