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Air is forced down a pipe by a powerful fan. A filter with considerable wind resistance can be alternately mounted inside the pipe at either end. Will the same amount of air throughput occur with the filter mounted at either end?

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Yes. Here's how to understand this: we model the duct as a very small resistor and the filter as a much larger one. We model the fan as a source of voltage (analogous to the pressure developed by the fan blades). These three elements are in series, so the same flow flow that goes through any one of them necessarily flows through all the others. This in turn means that the flow through the series connection does not depend on the order of the elements in it.

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