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Problem 57 Hard Difficulty

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P 18.57). The unknown resistance $R_{x}$ is between points $C$ and $E$ . Point $E$ is a "true ground" but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth’s surface. Two identical rods are driven into the ground at $A$ and $B$ , introducing an unknown resistance $R_{r}$ The procedure for finding the unknown resistance $R_{x}$ is as follows. Measure resistance $R_{1}$ between points $A$ and $B$ . Then connect $A$ and $B$ with a heavy conducting wire and measure resistance $R_{2}$ between points $A$ and $C$ . (a) Derive a formula for $R_{x}$ in terms of the observable resistances $R_{1}$ and $R_{2} .$ (b) A satisfactory ground resistance would be $R_{x}<2.0 \Omega .$ Is the grounding of the station adequate if measurements give $R_{1}=13 \Omega$ and $R_{2}=6.0 \Omega ?$

Answer

a. R_{x}=R_{2}-\frac{R_{1}}{4}
b. no answer available

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Video Transcript

in the first quarter of this question we're going to derive for formula for Rx in terms of the human resistance is our one and two that is addict. Let's call the equal distance from my toe. Bees are one then we can right are one equals two r y plus our Why so it will be close to you are why so are y can be written, as are y equals to one by two Are one the school it equation one. Now let's kill Fred. I collect resistance from my toe point c Yes, to our Why are in panel So their equipment is a sense Will be r e y equals to one by two are white No, these are the wise In Siri's we are too. So we can write over direct story so we can write two equals to Ari Why plus Rx no sitting the William for deciding why into this equation and the soul of this equation for Rx we will get thanks you close to our two minus one by two are Why now Sitting the well You off this our wife from equation One Into this equation, we can write Rx calls to our two minus into minus one by two into one by two or one. So this can't be the Internet. Our X equals two two, minus one by four. I want So this is the required formula. In part b of this question, we have to kill Claire the numerical value for this Rx. So let's try the values off. These are one and are too into a low for Mona, That is our X equals toward two minus one before I want no, by sitting away use even get our X equals 26 points in omega minus one by four into 13 omega. So this will give us our x equals two to point it omega as a developer off Rx, which is too pointed. Well, maybe, uh, excuse the prospective value for X. So we can say that it is not so terribly grounded. Thank you.

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Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Aspen F.

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Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp