# HW12 - MasteringPhysics 3:42 PM Assignment Display Mode...

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5/10/09 3:42 PM MasteringPhysics Page 1 of 10 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers phy260S09 HW12 Due at 11:00pm on Tuesday, May 12, 2009 View Grading Details Capacitors in Series Description: Contains several questions that help practice basic calculations for capacitors connected in series; there is a similar skill-builder ("Capacitors in Parallel") about capacitors connected in parallel. Learning Goal: To understand how to calculate capacitance, voltage, and charge for a combination of capacitors connected in series. Consider the combination of capacitors shown in the figure. Three capacitors are connected to each other in series, and then to the battery. The values of the capacitances are , , and , and the applied voltage is . Initially, all of the capacitors are completely discharged; after the battery is connected, the charge on plate 1 is . Part A What are the charges on plates 3 and 6? Hint A.1 Charges on capacitors connected in series When the plates of two adjacent capacitors are connected, the sum of the charges on the two plates must remain zero, since the pair is isolated from the rest of the circuit; that is, and , where is the charge on plate . Hint A.2 The charges on a capacitor's plates When electrostatic equilibrium is reached, the charges on the two plates of a capacitor must have equal magnitude and opposite sign. ANSWER: and and and and 0 and 0 and Part B If the voltage across the first capacitor (the one with capacitance ) is , then what are the voltages across the second and third capacitors? Hint B.1 Definition of capacitance The capacitance is given by , where is the charge of the capacitor and is the voltage across it. Hint B.2 Charges on the capacitors As established earlier, the absolute value of the charge on each plate is : It is the same for all three capacitors and thus for all six plates. ANSWER: and and and 0 and [ Print ]
5/10/09 3:42 PM MasteringPhysics Page 2 of 10 http://session.masteringphysics.com/myct Part C Find the voltage across the first capacitor. Hint C.1 How to analyze voltages According to the law of conservation of energy, the sum of the voltages across the capacitors must equal the voltage of the battery. Express your answer in terms of . ANSWER: = Part D Find the charge on the first capacitor. Express your answer in terms of and . ANSWER: = Part E Using the value of just calculated, find the equivalent capacitance for this combination of capacitors in series. Hint E.1 Using the definition of capacitance The "equivalent" capacitor has the same charge as each of the individual capacitors: . Use the general formula to find . Express your answer in terms of . ANSWER:

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HW12 - MasteringPhysics 3:42 PM Assignment Display Mode...

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