Physics 208: Electricity and Magnetism. Exam 2, Secs. 501–505 2 March 2006Instructor: Dr. George R. Welch, 301D Doherty Bldg, 845-1571Print your name neatly:Last name:First name:Sign your name:Please fill in your Student ID number (UIN): – –IMPORTANTRead these directions carefully:• There are 7 problems totalling 100 points. Check your exam to make sure youhave all the pages. Work each problem on the page the problem is on. Youmay use the back. If you need extra pages, I have plenty up front.• Indicate what you are doing! We cannot give full credit for merely writingdown the answer. Neatness counts! I will give generous partial credit if Ican tell that you are on the right track. This means you must be neat andorganized.• Each problem with its associated figure is self explanatory. If you must aska question, then come to the front, being as discrete as possible so as not todisturb others.• Put your name on each page it is asked for. You will lose credit if you fail toprint your name on each page it is asked for.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 1. 15 points.(a) In the resistor network shown, all the individual resistors have the same resistance R. Cal-culate the resistance between points A and B. Express your answer in terms of R and numericalquantities.RR RRRRA B(b) Suppose you have been handed four capacitors, whose capacitances are exactly 3.0 µF,5.0 µF, 6.0 µF, and 8.0 µF. Show a way to obtain an equivalent capacitance of exactly 7.0 µF usingsome or all of these capacitors.Be neat. Neatness helps. Work neatly.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 2. 15 points.A battery with EMF given by V is connected to two capacitors C1and C2as shown.C1C2V(a) Calculate the charge on each capacitor.(b) Calculate the potential difference across each capacitor.(c) Calculate the total energy stored in the two capacitors.Express all your answers in terms of V , C1, C2, and numerical factors.If you work neatly I will find more partial credit for you!Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 3. 10 points.A battery with EMF given by V is connected to two resistors R1and R2in two ways as shownin the two figures.R1R2R1R2VV(a) (b)Calculate the total power dissipated in the resistors for each of the two cases (a) and (b). Indicatewhich one is larger.Make sure you are being neat. Working neatly will help you get it right.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 4. (10 points)Two batteries with EMF given by V1and V2are connected with two resistors R1and R2asshown in the Figure.V1V2R2R1(a) Derive an expression for the current that is flowing in this circuit. Express your answer interms of V1, V2, R1, R2, and numerical factors.(b) Suppose that V1= 10 V, V2= 20 V, R1= 10 Ω, and R2= 10 Ω. Calculate the current inAmperes, and indicate if it is clockwise or anticlockwise.Work neatly! If you are neat, I can read what you did.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 5. (20 points)In the circuit shown below, there are three batteries and three resistors. Two of the batterieshave EMF equal to 10 V and the third is 20 V. All of the resistors have the same resistance of 10 Ω.Calculate the current in each resistor. Make sure you make it clear which is which! Forexample, you could say which is right, center, and left. Similarly, you could call them 1, 2, and3, but you must clearly indicate which is which. You must also make it clear which direction thecurrent is flowing in each case.10Ω 10Ω 10Ω20 V10 V 10 VIMPORTANT: You must write your equations neatly! I will not give full credit unless yourequations and answers are neat and organized.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 6. (15 points)Consider the circuit shown below. The battery has EMF given by V , the capacitor has capaci-tance C, and all three of the resistors have the same resistance R.SVRRRC(a) Suppose that the switch S is in the position shown above for a long time. Calculate thecharge on the capacitor. Express your answer in terms of V , C, R, and numerical factors.(b) Suppose that after the charge on the capacitor has equilibrated at the value you just calcu-ated, the switch S is flipped to the opposite position shown. We will call the time that the switchis flipped t = 0.Give an expression for the charge q(t) on the capacitor as a function of time. Express thefunction in terms of V , C, R, numerical factors, and, of course, t.NOTE: I don’t expect you to solve any integration, but you must indicate your thinking, andhow you got your result.You should be neat. You are more likely to get it right if you work neatly.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 7. (15 points)Consider the circuit shown b elow consisting of a battery with EMF given by V , two resistorsR1and R2, and two capacitors C1and C2.R1VSR1CC22(a) Suppose the switch S is open as shown, fora long time. Calculate the charge on each of thetwo capacitors.(b) Suppose the switch is closed for a long time.Now calculate the charge on each of the two ca-pacitors.In all cases, express your answers in terms ofV , R1, R2, C1, C2, and numerical factors.Working neatly will help you think about what you are