Potential Difference across a resistance

[Differentiate1]

Homework Statement

a) Find Req of the circuit
b) Find the potential difference across resistance R3[/B]

Homework Equations

Resistors in parallel = (1/R1 + 1/R2 + 1/R3 + ...)^-1
Resistors in series = R1 + R2 + R3 + ...

The Attempt at a Solution

a)
R3 and R4 are in parallel --> [ (1/40Ω) + (1/50Ω) ]^-1 = 200/9 Ω
R2 and R_34 are then in series --> 50Ω + (200/9)Ω = 650/9 Ω
R1 and R_234 are then in parallel --> [ (1/40) + (650/9) ]^-1 = 25.7Ω

b)
This is the part I need help with as I'm clueless on even how to start. Any guide is appreciated.

 

[Orodruin]

How is the potential split between two resistances in series?

 

[Differentiate1]

How is the potential split between two resistances in series?

In series, the potential is equal to the sum of the individual voltages I recall. So Vtot = V1 + V2 + ...

 

[Orodruin]

Yes, and how would you find the individual voltages?

 

[Differentiate1]

Yes, and how would you find the individual voltages?

Using Ohm's Law, V = IR --> I would say find the current first. So I = V/R.
Vtotal = 10 V here --> I = 10V/Rtotal = 10/26
V1 = I(R1)
V2 = I(R2)
V4 = I(R4)
Then, V3 = I(R3) = 15.38 V

The answer however is 5.5 V.

 

[Orodruin]

The current you have computed is the total current through the equivalent circuit, not the current through R3.

 

[Differentiate1]

The current you have computed is the total current through the equivalent circuit, not the current through R3.

I am unsure of how to find the current through R3, the individual resistor.

 

[Orodruin]

You do not need to. There are several ways of approaching this and the one I had in mind does not rely upon it. Let us try another one: Can you find a relation between the potential across R2 and that across R3?

 

[Differentiate1]

You do not need to. There are several ways of approaching this and the one I had in mind does not rely upon it. Let us try another one: Can you find a relation between the potential across R2 and that across R3?

Well since R2 and R3 are in series, V23 = V2 + V3

 

[Orodruin]

And what does it have to equal to?

 

[Differentiate1]

And what does it have to equal to?

Since this is a closed loop, V23 would have to equal 0.

 

[Orodruin]

You can use Kirchoff's laws for sure. However, you are not closing a loop by going across R2 and R3. In order to close it, what other component do you need to cross? (There are two choices, one is simpler than the other...)

 

[Differentiate1]

You can use Kirchoff's laws for sure. However, you are not closing a loop by going across R2 and R3. In order to close it, what other component do you need to cross? (There are two choices, one is simpler than the other...)

Would need to cross R1 to close it?

 

[Orodruin]

Yes, or ... (You picked the slightly more complicated choice)

Alternatively, what is the potential difference across R1?

 

[Differentiate1]

Yes, or ... (You picked the slightly more complicated choice)

Alternatively, what is the potential difference across R1?

I = 10/26
So V1 = (10/26)(40) = 15.38 V

 

[Orodruin]

No. All the current does not go through R1 either. You do not need to know the current to know the voltage across R1, it is enough to use Kirchoff's voltage law.

 

[Differentiate1]

So would I set V1 + V2 + V3 - 10 = 0 ?

 

[Orodruin]

No, you are now confusing two of the loops for KVL. Just use one loop at a time.

 

[Differentiate1]

No, you are now confusing two of the loops for KVL. Just use one loop at a time.

For R1: V1 would have to be 10V. Need to clarify that before moving on.

 

[Orodruin]

Correct. So what does this tell you about V2 and V3?

 

[Differentiate1]

V2 + V3 would have to equal 0?

 

[Orodruin]

No. What loop are you getting this from?

 

[Differentiate1]

Just redid it.
V1 - I2(R2) - I3(R3) = 0
--> I2(R2) - I3(R3) = 10 V
This next step correct?

 

[Orodruin]

You have made a mistake in solving for V2 + V3. I also strongly suggest you work with the voltages instead of the currents, since you are looking for a voltage.

Once you have solved it correctly, ask yourself what the current through R2 is and how you can use this to find V2 and thus V3.

I am now going to bed so this is my last post for today, it is 4 am here.

 

[Differentiate1]

You have made a mistake in solving for V2 + V3. I also strongly suggest you work with the voltages instead of the currents, since you are looking for a voltage.

Once you have solved it correctly, ask yourself what the current through R2 is and how you can use this to find V2 and thus V3.

I am now going to bed so this is my last post for today, it is 4 am here.

Alright thanks again. I'll see what I can work with.