## Finding Current, Voltage, and Resistance in Parallel Circuits

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?
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 Recognitions: Gold Member Science Advisor Staff Emeritus Start by considering the relationship between I0 and the current in the two branches.
 So would this be right? I0 = I1 + I2 I2 = 6 - 2 I2 = 3 A

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Homework Help

## Finding Current, Voltage, and Resistance in Parallel Circuits

 Quote by PrincessPerry So would this be right? I0 = I1 + I2 I2 = 6 - 2 I2 = 3 A
It looks fine. What else can you find now that you have I2?

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

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

 Quote by gneill What's left to solve for? Do you have enough information now to calculate it?
I need to find the value for V0. And to do that, I need to find R0.

Recognitions:
Homework Help
 Quote by PrincessPerry I need to find the value for V0. And to do that, I need to find R0.
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?

 Quote by 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?
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.

 Recognitions: Homework Help 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?

Recognitions:
Gold Member
Staff Emeritus
 Quote by PrincessPerry So would this be right? I0 = I1 + I2 I2 = 6 - 2 I2 = 3 A
Since when does 6-2=3?

 Quote by Janus Since when does 6-2=3?
My careless mistake. So that changes things then.
Since I2 = 4 A, that means:
V2 = 36 V
R1 = 18 Ω
and
Rp = 6 Ω

 Quote by 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?
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?

 Quote by 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?
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.

 Tags current, parallel circuit, resistance, voltage