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PHYS202SP200826

PHYS202SP200826 - PHYS202SP2008 Week 7 part 1 Due at 6:00pm...

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PHYS202SP2008 Week 7 - part 1 Due at 6:00pm on Wednesday, May 14, 2008 View Grading Details Capacitors in Parallel Learning Goal: To understand how to calculate capacitance, voltage, and charge for a parallel combination of capacitors. Frequently, several capacitors are connected together to form a collection of capacitors. We may be interested in determining the overall capacitance of such a collection. The simplest configuration to analyze involves capacitors connected in series or in parallel. More complicated setups can often (though not always!) be treated by combining the rules for these two cases. Consider the example of a parallel combination of capacitors: Three capacitors are connected to each other and to a battery as shown in the figure. The individual capacitances are , , and , and the battery's voltage is . Part A If the potential of plate 1 is , then, in equilibrium, what are the potentials of plates 3 and 6? Assume that the negative terminal of the battery is at zero potential. Hint A.1 Electrostatic equilibrium When electrostatic equilibrium is reached, all objects connected by a conductor (by wires, for example) must have the same potential. Which plates on this diagram are at the same potential? ANSWER: and

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Capacitors in Parallel Part A and and and Part B If the charge of the first capacitor (the one with capacitance ) is , then what are the charges of the second and third capacitors? Hint B.1 Capacitance is given by , where is the charge of the capacitor and is the voltage across it. Hint B.2 As established earlier, the voltage across each capacitor is . The voltage is always the same for capacitors connected in parallel. ANSWER: and and and and
Capacitors in Parallel Part A Part C Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three individual capacitors calculated in the previous part, find the total charge for this equivalent capacitor. Express your answer in terms of and . ANSWER: = Part D Using the value of , find the equivalent capacitance for this combination of capacitors. Hint D.1 Using the definition of capacitance Hint not displayed Express your answer in terms of . ANSWER: = The formula for combining three capacitors in parallel is . How do you think this formula may be generalized to capacitors?

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Capacitors in Series 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 .
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