A machine part has a resistor X protruding from an opening in the side. This resistor is connected to three other resistors, as shown in Fig. E26.2. An ohmmeter connected across a and b reads 2.00 Ω.

What is the resistance of X?

Video transcript

Hi everyone today we are going to determine the value of the unknown resistance. R. Which is given here when an unknown resistor is actually connected with three other resistors. As shown here with equivalent resistance across P. And Q. Measure to be six. Oh okay so recall that the equivalent resistance of serious resistor. So in series our key is going to equals to just essentially the sum the summation of all the R. I'm just gonna write R. N. Here. Just like so well in parallel are a key or essentially I think it's gonna be easier this way are key is going one over R. E. Key is gonna be one over R one plus one over R. Two plus one over R. N. So these are pretty much all that we needed to solve this problem. We know that our total R. P. Q. Is going to be six right? And we just have to find what are is okay. The way we want to solve for this is to actually solve for the equivalent resistance between P. Q. And equated to six. And then solve for the unknown resistance of our. Now we probably want to start by redrawing the circuit in a more easy to visualize form. So we have essentially two series resistors here. I'm just going to redraw this so that it's easier for you guys. So there's this 14 m. here and then there will be a different one which is also is going to be 15 homes and there will be Another one here which is going to be 13 mm. And then this is gonna be the p the Q. And last one which is gonna be the R. So looking at it this way, we know that the 14 and the 15 homes are in series and then it is going to be in peril with our 13. Um and those two in series. Okay so first we want to start by calculating the equivalent for this combination here. So our series it's going to be 14 plus 15 which is equals to 29. Oh and then the R. P. Q. Is then going to be one over r. p. q. Equals to one over the first capacitor, the first resistor in parallel one over R. Plus 1/13 plus 1/29. Just like so and then we know that the R. P. Q. Here is going to be 1/6 because the R. P. Q. Is six. So essentially one over R. Is then going to be 1/6 minus 1/13 minus 1/29 which is going to be um simplifying everything, is then going to be 1 25/ to 6. To just like so so then we know that the R. Is just gonna be the reverse of this which is going to be 2 to 6 to over 1 25. Just like so and this will go over in an hour of 18.1. That will be the answer for this problem which is going to be option D. Just like so. Okay, if you guys still have any question on this, make sure to check out other videos regarding this topic because we have similar videos on this, similar topics. And yeah, that will be all for this particular practice problem. Thank you.