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The circuit above has two resistors in parallel. The first, $R_{1}$ , will have its resistance steadily increased. The second, $R_{2}$ , will have a constant resistance of $R_{2}=4 \Omega .$ Which of the following graphs correctly depicts the total resistance of the circuit, $R_{\mathrm{T}}$ , as a function of $R_{1} ?$a. IMAGE IS NOT AVAILABLE TO COPYb. IMAGE IS NOT AVAILABLE TO COPYc. IMAGE IS NOT AVAILABLE TO COPYd. IMAGE IS NOT AVAILABLE TO COPY

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Mhm. One of the examples that shows up a lot in circuits is a situation where you look at a circuit with short term behavior with time T. Equals zero, for example after switches closed and then after a long time um when the switch has been closed for a very long time. Um And these are usually a fairly simple to analyze. We'll take a look at a simple example here where you have two resistors in parallel and one is just we'll call are one and the other is for OEMs and instead of closing a switch, what we're going to do is let our one increase as time goes to infinity let's say. Um And we we don't know where it starts from but we can look at it as a very situation where it starts with a very low value close to zero for example. Um And if it starts with our one very low at T. Equals to zero. So usually what you do is you re draw the circuit at two different times. Um And we're gonna start with our one very close to zero, which is we'll see is it's not a good idea what your circuit is basically going to look like is a short between The two terminals of the battery. Okay. Um Mhm. So it's going to act like that total resistance in the circuit Is also very close to zero At T. equals zero. And like I said, that's not a very good idea because that could battery out. And of course we know shorted batteries can create fires and whatnot. Um But then as time goes to infinity, we're going to let are also that same re sister become infinitely large. And what that will look like then is I'll call it the open circuit. Okay. So you might as well have no connection whatsoever between those two points in the circuit. Um and then you're, our total is just going to look like for OEMs. Um, so what your total resistance will look like in time, uh, is it will start at a low value. Maybe not perfectly zero. We hope not. And it will approach for OEMs. The larger that are one gets, the more that circuit will approach the Forum limit. Mm hmm. So almost like calculus taking a limit. Mm

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