In the figure below are shown four identical capacitors and two identical batter
ID: 1541669 • Letter: I
Question
In the figure below are shown four identical capacitors and two identical batteries connected in series and parallel, ranking the variables for the four capacitors. Once you have decided on your ranking for each problem, select the numbers of the capacitors (C1, C2, C3, and C4) and the relational operators (GT to mean greater than, and EQ to mean equal) that produces the correct ordering for each variable. (If two or more are equal, always put them in numerical order in the string so the auto grading will give you the proper credit.) A. What is tie ranking of tie voltage drops across the capacitors? B. What is the ranking of the magnitudes of the electric fields inside the capacitors? C. What is the ranking of the energy stored in the capacitors? D. What is the ranking of the net charge on each capacitor? A capacitor stores a separation of charge. Since to separate the charges on a capacitor, you have to move charges against where the E field wants to push them, charging takes work. That work becomes stored energy -- just like carrying water up a hill so that you can let it roll down at a later time and turn a generator. A. Suppose the charges on the capacitor plates are equal to +q and -q. How much work does it take to carry a small positive charge p from the negative plate to the positive one, thereby increasing the charge on the plates slightly? Express your answer in terms of p, the amount of charge on each capacitor plate at the time, q (recall there is +q on one side, -q on the other), and the capacitance of the capacitor, C Work = Explain your reasoning. B. If you start with no charge on the plates and start to carry small charges over a bit at a time, the total charge Q will increase. Since the potential difference is proportional to the charge on each plate, the graph of the potential difference vs. the amount of charge on the plate will be a straight line, as shown by the dotted line on the graph at the right. From the geometry of this figure, find an expression for the total amount work it takes to charge the plates up to a value of + Q, -Q. This is equal to the energy stored in the capacitor by the separation of positive and negative charges. Express your answer as a function of Q and C. Energy stored in capacitor = Express your answer as a function of C and V, the voltage difference between the plates. Energy stored in capacitor = Explain how you got your results to part B.Explanation / Answer
V3 = V4 > V1 = V2
V3 EQ V4 GT V1 EQ V2
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B)
E = V/d
E3 = E4 > E1 = E2
E3 EQ E4 GT E1 EQ E2
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energy = (1/2)*C*V^2
(C)
U3 = U4 > U1 = U2
U3 EQ U4 GT U1 EQ U2
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Q = C*V
(D)
Q3 = Q4 > Q1 = q2
Q3 EQ Q4 GT Q1 EQ Q2
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work dw = dV*p = q/C*p = qp/C
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energy U = (1/2)*Q^2/C
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U = (1/2)*C*V^2
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U = (1/2)*Q*V