# calculate potential difference

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

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Author Commented:
how much is I1 and I2 ?

is the I = Sigma ( Emf) / Sigma (R)   correct ?
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Author Commented:
why isnt the  Vab = 42- (2*2)=38 V   correct ?

thanks.

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Commented:
you have 3 equations in 3 unknowns to solve simultaneously
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Commented:

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 Commented:
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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Commented:
Well, it depends on which direction you measure the current, but I had it set up with a positive answer
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Commented:
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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