Solve each problem. Current FlowIn electric current flow, it is f...

Question

Solve each problem. Current FlowIn electric current flow, it is found that the resistance offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire 0.01 in. in diameter has a resistance of 0.4 ohm, what is the resistance of a wire of the same length and material with diameter 0.03 in., to the nearest ten-thousandth of an ohm?

Accepted Answer

An aluminum rod elongate when subjected to a pulling force for a certain length and pulling force. The elongation varies inversely as a square of the diameter. When a specific pulling force is exerted on the 30 millimeters diameter rod elongates by six millimeters. Considering the same force, calculate the elongation of a 50 millimeters rod. Possible answers being 2.161 point 720.96 and 3.24 all in millimeters. So our first key here is to notice elongation varies inversely as the square of the diameter, we have our elongation E since it varies inversely as a square, a diameter, we all said this is equals to one over D squared, which is diameter. Now we want variation. So we will multiply our entire right side by some constant K K A E equals K over D square. Now we can solve for K to get the general constant, we have the elongation of six millimeters when we have a millimeter diameter, right. So define K, we have eight equals six set that equals to K divided by 30 millimeters squared. We get six equals K divided by multiplying 900 on both sides gives us K equals 5400. Now that we have our constant K, we can plug this into our original equation to find our new elongation. We have key equals K which is now divided by our new diameter, which is 50 squared, we get E equals 5400 divided by 2500, which simplifies to about 2.16 millimeters. We then say the answer to our problem is answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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