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Topic: Battery Problem - With Loop Rule (pic attached)  (Read 6365 times)

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Offline aleksxxx

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Battery Problem - With Loop Rule (pic attached)
« on: March 11, 2007, 01:05:15 PM »
Here is the problem

"lets set the internal resistance, ri, of the battery with emf Ei. equal to bEi where b is a constant assumed the same for all three batteries.


2.To decrease internal resistance we can connect the batteries in parallel, although this advantage could be offest by a decrease in net voltage. To test this hypothesis find the current flowing through the 200 ohm resistor, assume 'b' is the same from part one.

2. Relevant equations
Kirchoffs's (sp) Loop Rule

3. The attempt at a solution

Ok - For part one i set up the loop rule equation as follows:

After substituting in the EMFs and resistances i got the equation:
-2.6= -.137bE1 - .137bE2 - .137bE3

From there i factored out the .137 and brought that to the other side and then factored out the 'b' and got:

Im not sure i did that first part right, becuase for the second part when i figure out all the currents, I1, I2, I3, they all come out to the same thing becuase the equation, I=E/R, and R=bE, the EMFs just cancel giving me 1/b for each current, 1.7A=I1=I2=I3.

Then using I=5.1A solving for the deltaV across the 200ohm resistor i get:
DeltaV=(5.1A)(200ohms)=1020V (WAYYY too high)

Im not sure where im going wrong here...i tried this and another way and i still get a deltaV higher than the combined voltages of the three batteries

----the other way i tried the problem was like this:

using the equation: E=IR
I took the EMF of the first battery, 5v, and set the equation as follows:

5V=(.137A)(r1) ==> where r1=bE1

Using that value in the second part of the problem still gives me a voltage drop of 82V across that 200ohm resistor, which cant be correct.

Offline Borek

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Re: Battery Problem - With Loop Rule (pic attached)
« Reply #1 on: March 11, 2007, 05:52:43 PM »
1. Where have you lost I when solving for b? There were two unknows (b & I) yet somehow you have calculated b value from the equation. Or was I given, you just forgot tp mention it?

2. Please write all equations describing the circuit. There are 4 unknowns - total current and three 'subcurrents" in three branches. Thus you need four equations. Or there are 5 unknowns (4 currents plus b) but I think you have to treat bas a parameter and compare total currents in both cases as a function of b.
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