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Resistance

 
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roxiney



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

PostPosted: Thu Sep 30, 2010 9:20 pm    Post subject: Resistance Reply with quote

When a 27.0-V 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

PostPosted: Fri Oct 01, 2010 7:17 pm    Post subject: Reply with quote

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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