Electrical RelationshipsDate: 12/10/96 at 17:30:06 From: MR MICHAEL FISHMAN Subject: Algebra 2 / Advanced Algebra Hi, I am currently taking Algebra 2 / Advanced Algebra. I have tried many different procedures to solve this problem but have failed each time. Here it is: The resistance R in an electrical circuit is related to the diameter d of the wire and the length L of the wire. In an experiment, John obtained the following data with a 50 ft. wire: Diameter (inches) .05 .08 .11 .14 .17 .2 Resistance (ohms) 9.0 3.5 1.9 1.1 0.8 0.6 How does R vary with d? I believe the answer is supposed to be jointly, directly, or indirectly, or something along those lines. However, since no formula was provided, I need to determine that first before I can tell if it's direct, indirect, joint, etc. I have tried numerous things. I know that whatever the formula is, it will equal R. In this case, I chose .05 and 9. I tried .05*50, 50/.05, .05/50. I cannot seem to come out with 9. I also tried the same formulas with .08 and 50, but failed to get 3.5. Can you help me figure this out? Thanks a lot for the help, and keep up the good work! Mike Date: 12/11/96 at 20:58:31 From: Doctor Rob Subject: Re: Algebra 2 / Advanced Algebra Well, first of all, it is clear that R varies inversely with d, because when d gets bigger, R gets smaller. For a fixed value of L, R will equal some function of d which gets smaller as d gets larger. This will eliminate things like a positive constant times d, which must vary directly with d, not inversely. You can try C/d, where C is a constant. Picking any of the above points will allow you to compute C at that point. Then you can test by checking other points. If this doesn't check, try a constant over some other function of d. Note that the value of L doesn't matter for this problem since it is the same at every point used in the experiment. Another way to proceed is the following: If you suspect that R = C*d^n for some n, you can take logarithms of both sides of this equation to get: log R = log C + n*log d By plotting points (log d, log R) on a graph, you should be able to see a straight line with slope n and log C as its (log R)-intercept. Once you get n and C, you can test the points from the experiment to see if they are close to the values for this function. If so, then the formula R = C*d^n is a correct guess. If not, then the function you seek must have another form, perhaps C*e^(-n*d), or C/log d, or something else. If you need more assistance, please write back. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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