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calculate potential difference

Posted on 2006-11-03
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Last Modified: 2008-02-26
i have the sketch :
emf1=28 , enf2=42 V. R1=2 , R2=5 and R3=1
Calculate the potential difference Va-Vb betwwen points A and B

_________| |______________/\/\/\/\/\/\__________
|                E1                            R1                               |
|                                                                           |
|                                                                           |
|                 E2                             R2                             |
A__________| | ___________/\/\/\/\/\______________  B
|                                                                            |
|                                                     R3                        
_________________________/\/\/\/\/\/\/\__________|



solution that i tried :


I = Sigma ( Emf) / Sigma (R)

and Vab = 42- (2*2)=38 V

is it correct ?
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Question by:c_hockland
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LVL 84

Expert Comment

by:ozo
ID: 17871990
vAB = (I1+I2)*R3
    = E1 - I1*R1
    = E2 - I2*R2

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Author Comment

by:c_hockland
ID: 17871997
how much is I1 and I2 ?

is the I = Sigma ( Emf) / Sigma (R)   correct ?
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Author Comment

by:c_hockland
ID: 17872004
why isnt the  Vab = 42- (2*2)=38 V   correct ?

thanks.
 
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Expert Comment

by:ozo
ID: 17872019
you have 3 equations in 3 unknowns to solve simultaneously
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LVL 27

Expert Comment

by:d-glitch
ID: 17872024
I am pretty sure your answer is wrong.

What is Sigma?  What is your method of solution?  
Have you studied Superposition yet?

Set E2 to zero (a short circuit) and solve the circuit.  ==>  Find the current through R3.
Set E1 to zero (a short circuit) and solve the circuit.  ==>  Find the current through R3.

Add up the two values to find the net current in R3 for the original circuit.
This will let find the voltage across R3, which is the answer to your question.
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Author Comment

by:c_hockland
ID: 17872029
ok, i did solve the system

vAB = (I1+I2)*R3
    = E1 - I1*R1
    = E2 - I2*R2


and I1= negative ..is it correct or it doesnt make sense to have a negative value ?
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Accepted Solution

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ozo earned 500 total points
ID: 17872041
Well, it depends on which direction you measure the current, but I had it set up with a positive answer
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LVL 27

Expert Comment

by:d-glitch
ID: 17873640
This is a linear system so you can use Superposition:

The component of Vab due to E1 is:     E1*(R2||R3)/(R1 + (R2||R3))  =  28*(0.294)  =  8.235 V

The component of Vab due to E2 is:     E2*(R1||R3)/(R2 + (R1||R3))  =  42*(0.118)  =  4.941 V

Adding the two components  ==>  Vab = 13.176 V

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