Solve Vo Using Superposition Theorem for Circuit

[vs55]

Homework Statement

Use the superposition theorem to find Vo in the circuit

Homework Equations

The Attempt at a Solution

i made 8A source 0 so the first equation using KVL becomes:
10i1 = -20
i1 = -2
then making the 20V source 0, the next KVL equation becomes:
i think it's 5i2-8 = 0
i2 = 8/5

i think I'm messing up the second equation with the 20V source as 0...

 

[vs55]

ok i got the answer it but I'm still kind of confused. The first formula stays the same, in the second formula V would just be 8 x 2 = 16 and 16 + (-2 x 2) = 12 which is the answer. My question is for the first formula i chose the current arbitrarily(clockwise), and if i chose it to go the other way i would get the wrong answer. So how do i know what way to make the current flow for KVL?

 

[Tweedle_Dee]

It looks to me like your second formula is still incorrect. You should keep the two currents going in the same direction. The first current is clockwise (although its easier to keep the signs straight if you go counter-clockwise in this case) so you get -2A as you said. In the second case, you wouldn't have 8A going through the 2ohms.

Remember you have two loops with equal resistances, so your 8A source is going to be cut in half. And since you chose clockwise, you need to change the sign of your final answer so it matches the voltage orientation across the 2 ohm resistor.

Hope that helps.