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Problem Set 11

Problem Set 11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Turn in at your table during class labeled with your name and group (e.g. L01 2B) Problem Set 11 Due: Wednesday, November 21 st at beginning of class Problem 1: Where’s the energy go? Consider a simple RC circuit consisting of a “variable” battery (EMF 0 V or ε ), a resistor R and an uncharged capacitor C all in series. At time t=0 the battery is “turned on” (EMF ε ) and the capacitor is allowed to charge. A time T (>> RC ) later the battery is turned off (EMF 0 V) and the capacitor discharges. This process is continually repeated. (a) How much energy does the resistor dissipate while the capacitor is being charged (i.e. between t=0 and t= T )? (b) How does this compare to the amount of energy stored in the capacitor at time T ? (c) How much energy does the resistor dissipate while the capacitor is discharging (i.e. between t= T and t=2 T )? (d) What is the time average power dissipated by the resistor? Hint: To average a set of numbers you add the numbers and divide by the number you added. To average a periodic function, integrate it over one period and divide by the length (or in this case time ) of the period. Problem 2: Capacitor discharge You are tasked with designing a capacitor (capacitance C ) that will hold its charge for a long time. You want to make it using a dielectric with dielectric constant κ and resistivity ρ . That resistivity is a problem – even though it is high, it still allows charge to flow from one plate to the other over time. So you want to maximize the resistance between the plates. (a) Compare the resistance of the dielectric between the plates of a parallel plate, cylindrical and spherical capacitor, each with capacitance C but with whatever dimensions you want. HINT: Calculate RC and solve for R .
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