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Question
What is the $emf_s$ of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 V and the potentiometer balances for $R_x = 5.000 \Omega$ and $R_s = 2.500 \Omega$?
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Final Answer

$24.0 \textrm{ V}$

Solution Video

OpenStax College Physics Solution, Chapter 21, Problem 57 (Problems & Exercises) (1:43)

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Video Transcript
This is College Physics Answers with Shaun Dychko. With this potentiometer we have some standard EMF which is put in place of this to do a measurement of the resistance with the standard EMF. The standard EMF is going to be 12 volts. The resistance when the unknown EMF is in the circuit is five ohms. The resistance when the standard EMF is put in place here is two and a half ohms. So the EMF that's unknown equals this current whatever it is and we don't even care what it is, multiplied by the resistance here R x, and then when the standard EMF is there we have the same current because it's the same EMF here which we also don't know nor care about, we just care that it's the same in both cases. With both of the EMFs here we want this same EMF to be here so that the same current is flowing, which is why the current does not get a subscript x, nor does it get a subscript s because it's the same in both cases. The standard EMF is the current times resistance s. So, we take the ratio of these two and the currents cancel and we get R x over R s. That means the EMF that we don't know, EMF x, is going to be the standard EMF times R x over R s. So that's 12 volts times five ohms divided by two and a half ohms which is 24.0 volts.