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roxiney
Joined: 15 Sep 2010 Posts: 5 Location: north carolina

Posted: Thu Sep 30, 2010 9:20 pm Post subject: Resistance 


When a 27.0V emf device is placed across two resistors in series, a current of 12.0 A is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is 60.0 A. What is the magnitude of the larger of the two resistances? 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Fri Oct 01, 2010 7:17 pm Post subject: 


I don't understand what a 27 volt EMF device is? Is this some management speak for a battery? Can you write the question with more clarity please.
Anyway, I think that it is a question about resistance in series and parallel.
We know, for resistors in series,
R_tot = Ra + Rb
and Ohm's law, V = I R_tot
so, 27 = 12* (Ra + Rb)
or 27 = 12 Ra + 12 Rb (1)
In parallel,
1/R_tot = 1/Ra + 1/Rb = (Rb+ Ra)/(Ra Rb)
R_tot = Ra Rb / (Rb + Ra)
Using the same Ohm's law,
27 = 60 (Ra Rb / (Rb + Ra)) (2)
From eq. 1 we can find Ra in terms of Rb.
ie. (27  12 Rb)/12 = Ra (3)
Insert this into equation (2)
and solve for Rb.
Hint. (Ra = 0.62 Ohm, Rb = 1.63 Ohm) or (Ra = 1.63 Ohm, Rb = 0.62 Ohm) depending on what you call Ra and Rb. 

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