Finding Current, Voltage, and Resistance in Parallel Circuits

PrincessPerry

1. The problem statement, all variables and given/known data
In the following circuit solve for V0, R1 and Rp.
I0 = 6 A
I1 = 2 A
R2 = 9 Ω

2. Relevant equations
R = V/I
1/Rp = 1/R1 + 1/R2

3. The attempt at a solution
I think you need to find the total voltage first, but how?

Attached Thumbnails

 

Janus

Start by considering the relationship between I₀ and the current in the two branches.

PrincessPerry

So would this be right?
I0 = I1 + I2
I2 = 6 - 2
I2 = 3 A

gneill

It looks fine. What else can you find now that you have I2?

PrincessPerry

Well now you can find V2.
V2=RI
V2=(9)(3)
V2=27 V

This means that V1=27 V as well because it's a parallel circuit.

R1=V1/I1
R1=27/2
R1=13.5 Ω

But what do you do now?

gneill

What's left to solve for? Do you have enough information now to calculate it?

PrincessPerry

I need to find the value for V0. And to do that, I need to find R0.

gneill

R0? What's that? I see an R2 and what is no doubt the R1 that you found a value for above. Maybe you're thinking of Rp, the resistance of R1 and R2 in parallel?

As for V0, isn't that the voltage to be assigned to the voltage source? If so, do you already have a value for the potential across the source?

PrincessPerry

Well yes, I already found Rp, which is 5.4 Ω.

No, I don't think I have a value for that. I just need to solve for V0. For that, I already know the current, which is 6A, but I don't know the resistance.

gneill

Isn't the battery in parallel with the resistances? You already used the voltage property of parallel branches when you determined the voltage across R1...

And isn't the Rp the net resistance that you're looking for?

Janus

Since when does 6-2=3?

PrincessPerry

My careless mistake. So that changes things then.
Since I2 = 4 A, that means:
V2 = 36 V
R1 = 18 Ω
and
Rp = 6 Ω

PrincessPerry

Well yeah. The values for V1 and V2 are 36 V in the parallel circuit. But V0 is perpendicular to the parallel branches...

So are you saying that Rp can be used to find the value for V0?

PrincessPerry

Wait, I think I got it. You're right. Rp is the net resistance and V0 has the same value as V1 and V2, which I've already calculated.

Thank you so much.