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Figure 1 shows the results of a laboratory experiment. A current of 110A was applied to a Copper cylindrical conductor during 30 minutes. The points represent the temperature rise measurements; the continuous line represents a mathematical approximation found by the students who did the test using the first order model described in class. The ambient temperature was approximately kept at an average of 25 C. a. Estimate the equilibrium temperature rise. (2p) b. Estimate the time constant (2p) c. Write an expression for the estimated curve (theta as a function of time) using the numerical results obtained in parts a and b. (2p) d. The wire diameter is 4.5 mm, approximately. Estimate a value for the equivalent convection factor, h in W/(m2-K). (2p) e. Your task is to predict the theta vs t curve using the same and laboratory set-up but with a current of 85 amps. Write an equation like the one you wrote in Part C for the new conductor assuming that h has the same value determined in Part d. Plot the estimate theta as a function of time. (2p) Note: You do NOT have to use MATLAB to do Part e. You can do it with your calculator and plot the curve on a linear-scaled plot paper, or EXCEL, or any other method you have. 120 100 80 60 40 20 500 1000 1500 2000 2500 3000 3500 Time in seconds Figure 1: Results of a wire heating experiment (notice the temperature reaches burning levels) a) A metallic wire of certain secret new alloy is known to have a coefficient alpha a=0.0038K1 at 20°C. The density and specific heat of the metal are unknown. The wire has circular section with an unknown diameter and is used to build a cable with a rated temperature of 65°C and a damage temperature of 150°C. The damage 14t = Kd was found experimentally using no initial current and an ambient temperature of 25°C. The result was: Kd = 2.5.106 amp².s Find Kd using the rated temperature as initial value. b) Find Kd for a wire with the same characteristics as the wire in a) but with a diameter 1.5 times the size of the wire used in part a. (Use the same initial temperature value used to find the value of Kd given above.) c) Plot the three damage curves using a log-log scale, indicating which curve corresponds to each case. a. Determine the HV-side fuses needed to protect a transformer bank with a total three-phase capacity of 3x333kVA, 13800-480 V in connection YnynO. Show and explain step by step the procedure you employ to solve this question. Choose between the type K and type T fuse curves given in class. Assume the transformer has a damage curve as the one given in class. [3p] b. Plot both, the fuse curves and the transformer damage curve on the same log-log graphic. Use the log-log curve posted in the class web page. You do NOT need to use MATLAB to do this problem. You can do it with your calculator and plotting the curve with pencil on the given log- log sheet. It is your choice. The current must be referred to HV side of the transformer bank. [3p] Note: assume the inrush can be represented by a point in the t vs I plot with I = 12 x transformer rated current t = 0.1 second 1000 1000 700 700 500 500 300 300 200 200 Refing Reting a - 100 100 70 70 50 50 30 30 20 20 10 10 97 7 8 5 = 33 3 N° 2 I - 7 7 .5 5 , 3 2 .2 , J .07 .07 .06 05 03 .03 .02 02 or or .5 T I 2 3 5 7 10 20 30 50 70 80 .5 7 - 2 3 5 7 10 20 30 50 70 8 $00 500 700 (e) CURRENT IN AMPERES (b) CURRENT IN AMPERES Fig. 41-Time-current characteristic curves for Type K (Fast) universal fuse links. No arcing time is included. (b) Total-clearing curves. These curves show the time (a) Melting curves. These curves show the minimum time required to melt the fusible required for any given current to melt the fuse link and clear the circuit. element, starting from an ambient temperature of 25C with no previous loading. 1000 1000 700 700 500 500 300 300 200 200 Reting Reting ane eng 100 100 70 70 50 50 30 30 20 20 o 10 7 7 5 5 is *3 2 N° F I I , , 5 ,5 3 , 2 2 1 J 07 .07 os .05 03 03 02 . a DI DE 5 7 I 2 , 5 7 o 20 30 50 70 80 , , - 2 3 5 7 o 20 30 50 70 8 CURRENT IN AMPERES CURRENT IN AMPERES (a) Melting Curves (b) Total Clearing Curves Fig. 42-Time-current characteristic curves for Type T (Slow) universal fuse links. No arcing time is included. (b) Total-clearing curves. These curves show the time re- (a) Melting curves. These curves show the minimum time required to melt the fusible quired for any given current to melt the fuse link and clear the circuit. element, storting from on ambient temperature of 25C with no previous looding. TIME va CURRENT CURVE 1000.00 100.00 10.00 1.00 0.10 0.01 1 10 100 1000 10000 Current (Amps x ) e Volts

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