Finding Potential Difference Across AB in a Multi-Cell Circuit

[carlyn medona]

Homework Statement

Find potential difference across AB

Homework Equations

The Attempt at a Solution

I have posted a picture of my figure, I have 3-i1=v=2-i2=1-i3 and i1+i2+i3= io on solving I got 6-io=3v and then I found resistance equal to 1/3 ohm. So after solving I got v= 1 volt, but it's wrong

 

[cnh1995]

How much are ε₁ and ε₂? It is not clear from your images.

 

[carlyn medona]

E1= 3V E2 =2V and E3 = 1V each resistance = 1 ohm

 

[cnh1995]

E1= 3V E2 =2V and E3 = 1V each resistance = 1 ohm

Ok.
Let V_B=0V (ground reference).

Can you write KCL at point A in terms of V_A?

 

[carlyn medona]

Is KCL kirchhoff's current law?

 

[gneill]

Is KCL kirchhoff's current law?

Yes. You want to write the KCL node equation for node A.

 

[carlyn medona]

Io=i1+i2+i3

 

[cnh1995]

Io=i1+i2+i3

What would i₀ be?
How will you write the three currents in terms of V_A?