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Quiz+4+Section+D+-+Solution - D L SE C T I O N 7B.S11 Quiz...

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Unformatted text preview: D L SE C T I O N 7B.S11 - Quiz 4D Last 6 digits of student ID ______ _ Last name, ______________ Grade: first name: ______________ 04/27/2011 First three letters of your last name ___ N o boo k s o r not es. C a l c u l a t o r s O K . Show a l l you r w o r k b e l ow. A nsw e r s a l on e w i l l r e c e i v e no c r e d i t ! T h is q u i z h as t w o si d es! 1. You are at the McMurdo research center in Antarctica studying some of the unique lifeforms that live in unusually cold temperatures. The temperature outside at this time of the year is usually around -20o C, but you hear that a storm is coming and the temperature will slowly drop to some lower temperature. You need to finish the experiment and walk back to the main campus and want to make old when you leave. Your body produces energy as heat constantly (burning calories is how your body temperature is stably higher than the room temperature) and the power produced is 0.03 W . You have specially heavy clothes that are on average 5 c m thick (the average includes everything: boots, snow goggles, scarf, gloves, etc.) and the effective total surface area of the clothes is 3 m2. The conductivity k of the special material of your clothes is on average 7.5 10-6 W /(m K ). You will have to walk for a while to reach the main campus. To remain safe, you need to produce at least as much heat as you lose to the outside. Find the minimum temperature that you can safely walk in so that your body will be stably at 36o C and you can avoid getting hypothermia. You want to know when the heat produced by your body equals the heat lost to the atmosphere. Then you need to know what the heat flow is. This means that 0.03 W = I, where I is the heat flow to the atmosphere. j = -k Delta (T) / L = 7.5 x 10^(-6) W/(m K) x Delta(T) / 0.05 m 0.03 W = I = j A = Delta (T)_max x 4.5 x 10^(-4) W/K D elta (T)_max = 0.03/0.00045 K = 66.7 K = 66.7 C (in Delta's, C and K are the same) Delta (T)_max = 36 C - T_max = 66.7 C T_max = 36 C - 66.7 C = -30.7 C Thermal flux: Capacitor charging/discharging: 2. You have three circuits (label them 1, 2 and 3), each of the same type as the one shown to the right. Each battery has an identical . The values of the resistance and capacitance in each circuit is unknown. The capacitor is initially completely uncharged. You begin charging the capacitor in each circuit and you observe the current in each. The graph below shows the current in each circuit as a function of time starting the instant the capacitor begins to charge. a) Use the graph to rank the values of the resistance in each circuit from least to greatest. If any are equal specify that as well. Briefly explain your reasoning. D elta (V)_r = - I R at first Delta (V) is the same for all the circuits (because, like specified in the text, they h ave the same battery) then I=E/R where we used Delta (V)_r = - E. It is clear from the graph that circuits 3 and 2 start from the same I, so they also have the same R, while I_1 is smaller, meaning that R_1 is greater than R_2 = R_3 b) Use the graph to rank the time constants of each circuit from least to greatest (you can denote time constant ). If any are equal specify that as well. Briefly explain your reasoning. You can just read the graph for this. You know that the time constant is proportional to how fast the exponential drops. In this case, circuit 1 drops really fast (it becomes a half in 0.2 s), circuit 3 comes right after (it becomes half after about 1.5 s) and circuit 2 has the largest time constant. T_2 > T_3 > T_1 c) Use the results of parts a) and b) to rank the value of the capacitance in each circuit from least to greatest. If any are equal specify that as well. Briefly explain your reasoning. T_i = R_i C_i now, R_2 = R_3, but you know that T_2 > T_3, then C_2 > C_3 R_1 is the greatest, but T_1 is the smallest, then C_1 has to be the smallest in order to be multiplied to R_1 and still be smaller than T_3 and T_2 C_2 > C_3 > C_1 Thermal flux: Capacitor charging/discharging: ...
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