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Quiz+4+Section+C+-+Solution

# Quiz+4+Section+C+-+Solution - 7B.S11 Quiz 4C Last 6 digits...

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Unformatted text preview: 7B.S11 - Quiz 4C Last 6 digits of student ID ______ D L SE C T I O N _ Last name, ______________ Grade: 04/27/2011 first name: ______________ 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. Ruggero and the 7B class are working on an experiment at the McMurdo research center in Antarctica studying some of the unique lifeforms that live in unusuall y 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 -40o C . You need to make sure that the lab where the broken and the lab is not equipped to make up for its absence during particularly cold weather such as this incoming storm. The total power of the available heating system is 7800 W . The temperature of the lab needs to stay constantly at 5o C (you have been working with a coat on). You realize that there are rooms in the lab that are currently not needed for the experiment, so you decide to block their heater lines to redirect all the heat just to the important rooms, so that the heat lost can be compensated by the heat produced by the heater. Each room has an average of 150 m2 of wall surface area connecting the room with the external weather temperature. What is the maximum number of rooms that you can keep at 5o C when the outside temperature is -40o C ? The walls are 20 c m thick and their thermal conductivity is 3.5 10-2 W /(m K ). You know that the total amount of power cannot exceed the 7800 W that you have available. Each room requires the following power: j = - 3.5 x 10^(-2) W/(m K) x 45 K / 0.2 m = 7.9 W/m^2 I = j A = 150 m^2 x 7.9 W/m^2 I = 1181 W (per room) max_rooms = 7800/1181 = 6.6 ----> 6 rooms 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. The capacitors have all been fully charged using . The values of the resistance and capacitance in each circuit is unknown. You begin discharging 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 discharge. 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, like speciﬁed in the text, then I = Delta (V)_c / R where we used Delta (V)_r = - Delta (V)_c. It is clear from the graph that circuits 1 and 2 start from the same I, so they also have the same R, while I_3 is smaller, meaning that R_3 is greater than R_2 = R_1 b) Use the graph to rank the time constants of each circuit from least to greatest (you can denote t ime 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 3 drops really fast (it becomes a half in 0.2 s), circuit 2 comes right after (it becomes half in about 1.5 s) and circuit 1 has the largest time constant. T_1 > T_2 > T_3 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_1 = R_2, but you know that T_1 > T_2, then C_1 > C_2 R_3 is the greates, but T_3 is the smallest, then C_3 has to be the smallest in order to be multiplied to R_3 and still be smaller than T_1 and T_2 C_1 > C_2 > C_3 Thermal flux: Capacitor charging/discharging: ...
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