Finding Thevenin Voltage in a Complex Circuit

[sugz]

Homework Statement

The question is in the photo attached.

Homework Equations

The Attempt at a Solution

I have found the Thevenin voltage as the 10 and 20 ohm resistors are in series (30 ohms) and the 50 and 40 ohm resistor are in series (90ohms). The 30 and 90 ohm resistors are in parallel so

30||90 = (30×90)/(30+90) =22.5 ohms

I am having struggles with determine the Thevenin voltage as the solution says the 8 A current gets divided equally among the 10 and 20 ohm resistor but I don't understand why.

 

[gneill]

What is the total resistance of each branch (ignore the terminals A and B for the moment)?

 

[sugz]

60 ohms but how can we ignore terminals a and b?

 

[gneill]

60 ohms but how can we ignore terminals a and b?

I said ignore them for the moment. You can do this because they are open: not connected to anything so they do not pass any current.

So both of these branches have the same resistance, correct? The branches are in parallel, correct? How will current divide between equal resistances in parallel?

 

[sugz]

So since current doesn't pass through terminal a and b, they just flow down to the next resistor?

 

[gneill]

So since current doesn't pass through terminal a and b, they just flow down to the next resistor?

Yes. They are the only available paths.

 

[sugz]

Okay, that makes sense then, thank you!