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Show that if two resistors $R_{1}$ and $R_{2}$ are combined and one is much greater than the other $\left(R_{1}>>R_{2}\right) :$ (a) Their series resistance is very nearly equal to the greater resistance $R_{1}$ (b) Their parallel resistance is very nearly equal to smaller resistance $R_{2}$ .

refer solution

Physics 102 Electricity and Magnetism

Chapter 21

Circuits, Bioelectricity, and DC Instruments

Direct-Current Circuits

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

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Okay, let's look at the question with with some values. We don't know the values off our phone and are too. So let's assume that other one is 10,000 on 10,000 boom and are, too, which is supposed to be a very small compared to our one is one alone. Now let's look at the serious resistance. Serious resistance is simply addition off part one and not two. This is equal to 10,000 and one, which is very, very close to our one, as you can see. So it is indeed serious resistance equal to the greater resistance. Almost now for the part B. Let's use the same values so we know that it's one Divided by R P is equal to one about it back at once, plus one divided by our two. This will be equal to one divided by 10,000 plus one about it. But one this is equal to so now. One divided about 10,000 is simply 0.0 one plus one divided. That one is simply one. So this is equal to 1.1 So So the resistance in this case will be inverse off this value. So our P is equal to zero point 999 nine. So which is very close to one norm? As the questions is, the parallel resistance is very nearly equal to the Smallville distance are, too, which is equal to our two. Indeed, it means that the serious resistance for the this combination is almost equal to the larger one, and parallel little distance is almost equal to the small. Over this hole's Only when I won is much larger than our two. If they're comparable, that's 100,000. This will not hold that much. So this hole's only when one resistance is very large compared to other resistance.

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