In a circuit, a parallel combination of six 1.6-kΩ resistors is connected in series with a parallel combination of four 2.4-kΩ resistors. If the source voltage is 24 V, what will be the percentage of total current in one of the 2.4-kΩ resistors?
  1. 10%
  2. 12%
  3. 20%
  4. 25%
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OpenStax College Physics for AP® Courses, Chapter 21, Problem 2 (Test Prep for AP® Courses)

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This is College Physics Answers with Shaun Dychko. We have a circuit where there are six resistors in series connected to four resistors in parallel the resistors in parallel all have the same resistance and they are each 2.4 kiloohms although it turns out there's a lot of extraneous information in this question; it doesn't matter what the resistance of each of these resistors are in parallel, it just matters that they are all the same and I have labeled them R. There are six resistors here in series but their resistance also doesn't matter because we are not going to calculate what the current is, we are just going to calculate what percentage of the current goes through each of these resistors that are in parallel. So we know that there's going to be a current I 1 through the top resistor and then I 2 through this resistor here and I 3 through this resistor and I 4 through the bottom resistor but each of these currents are the same because there's some voltage across this collection of resistors connected in parallel each resistor experiences the same voltage drop because they are connected to the same beginning and end points and this is just a voltmeter to illustrate that there is V underscore P for 'parallel' this common voltage across each of these resistors and so they are all going to have the same current since they are all going to be this same voltage divided by the same resistance R so let's call this I P for current through a single resistor in parallel. The junction rule says that the total current coming in to this junction here must equal the total current coming out. Now since there four currents all of the same magnitude, we can say that the total current coming out is 4 times the current through one of the resistors and the total current coming in is I and so we can solve for the current through a single resistor by dividing both sides by 4 and then the current through the single resistor in parallel is the total current I over 4 and one quarter as a percentage is 25 percent, the answer is (d).