A uniform wire of resistance R is cut into three equal lengths. One of these is formed into a circle and connected between the other two (Fig. E26.1).

What is the resistance between the opposite ends a and b?

Video transcript

Hi everyone today we are going to determine the resistance of the circuit across terminal P and Q. So it is known here in this diagram that we have four different resistors with resistance R and R over three connected as shown in this diagram here. So we can know that first that this part right here is going to be in parallel with one another while the overall thing is then going to actually be in series wright recalled that the equivalent resistance of series resistors. So a series it's going to be R. E. Q equals two. R one plus R two plus R. N. So it's just a summation of all their sisters and then in parallel then it's going to be one over R. A Q is going to be one over R one plus one over R two plus one over r. n. So in this example we are required to determine the equivalent resistance of the entire circuit. So first what we want to do is to combine the two are over to your sister which are in parallel here with one other into one single sister. Okay, so one over R parallel will equal to one over R over three which is the first are over three and then the other one is also one over R over three, just like, so so in this case this is going to be three over R plus three over our so there will be six over our so our par is just going to be our over six. Okay, so now that we can convert this to its equivalent value which is r over six. We can do the whole series in Series, the whole circuit in series. Okay. So it will now consist of three different resistors. So our EQ is going to be our which is this first sister here plus our part which is our parallel equivalency are over six plus a different are here. So this will actually come up to be 2. r. And that will be the answer to our problem today, which is gonna be option B just like so if you guys are still confused and want more examples on this particular problem, we have other videos with similar topics so make sure to check it out and that will be all for this particular example. Thank you.