Finding Current, Voltage, and Resistance in Parallel Circuits

In summary, the circuit has a voltage of V2=27 V, a resistance of R1=13.5 Ω, and a potential across the battery of V1=36 V.
  • #1
PrincessPerry
8
0

Homework Statement


In the following circuit solve for V0, R1 and Rp.
I0 = 6 A
I1 = 2 A
R2 = 9 Ω

Homework Equations


R = V/I
1/Rp = 1/R1 + 1/R2

The Attempt at a Solution


I think you need to find the total voltage first, but how?
 

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  • #2
Start by considering the relationship between I0 and the current in the two branches.
 
  • #3
So would this be right?
I0 = I1 + I2
I2 = 6 - 2
I2 = 3 A
 
  • #4
PrincessPerry said:
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?
 
  • #5
gneill said:
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?
 
  • #6
What's left to solve for? Do you have enough information now to calculate it?
 
  • #7
gneill said:
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.
 
  • #8
PrincessPerry said:
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?
 
  • #9
gneill said:
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.
 
  • #10
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?
 
  • #11
PrincessPerry said:
So would this be right?
I0 = I1 + I2
I2 = 6 - 2
I2 = 3 A

Since when does 6-2=3?
 
  • #12
Janus said:
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
 
  • #13
gneill said:
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?
 
  • #14
gneill said:
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.
 

1. What is a parallel circuit?

A parallel circuit is a type of electrical circuit where multiple components are connected side by side, allowing the current to flow through different paths simultaneously. This results in a constant voltage across each component and the total current is divided among the branches.

2. How do you calculate total resistance in a parallel circuit?

The total resistance in a parallel circuit can be calculated by using the formula: RT = 1/(1/R1 + 1/R2 + 1/R3 + ...). This means that the reciprocal of the total resistance is equal to the sum of the reciprocals of each individual resistance.

3. What is the relationship between voltage and resistance in a parallel circuit?

In a parallel circuit, the voltage across each component is the same, while the resistance is inversely proportional to the current. This means that as the resistance increases, the current decreases, and vice versa.

4. How do you calculate total current in a parallel circuit?

The total current in a parallel circuit can be calculated by adding up the currents in each branch. This means that the total current is equal to the sum of the currents through each individual branch.

5. Can you have different voltage sources in a parallel circuit?

Yes, it is possible to have different voltage sources in a parallel circuit. Each voltage source will create its own branch in the circuit, and the total current will be divided among these branches. However, the voltage across each component will remain the same, regardless of the different voltage sources.

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