Calculate the current between point A and B

[meguco0314]

Homework Statement

[/B]

What is the current between points A and B?
The current I is unknown.
The voltage is 12V.
R1 = 3 Ohm
R2 = 6 Ohm
R3 = R4 = 4 Ohm

Homework Equations

U= R*I

The Attempt at a Solution

Total resistance from both branches:
1/R = 1/(R_1+R_3) + 1/(R_2+R_4)
1/R = 1/7 + 1/10
R = 1/(1/7 + 1/10) = 1/17/70 = 70/17 Ohm

Total current from both branches:
I = U/R = 12/(70/17) = 72/35 A

Here I get lost. Even If I can calculate the current that goes through each resistance (which I don't know how to do.) I don't know how I should determine how much current that goes from point A to B and/or vice versa.

 

[Qwertywerty]

Edit : First - Explain why you took R₁ and R₃ in parallel , and why you took R₂ and R₄ in parallel .

I noticed you had made a mistake . Hence the edit .

 

[Qwertywerty]

Please note my edited post .

 

[meguco0314]

Two resistors in a simple parallel connection - What is current in either ?

How do I determine the current in either? Can I use that 1/R = 1/R1 + 1/R2

Edit : First - Explain why you took R₁ and R₃ in parallel , and why you took R₂ and R₄ in parallel .

I noticed you had made a mistake . Hence the edit .

Do you refer to this:

1/R = 1/(R_1+R_3) + 1/(R_2+R_4)

Is this wrong?

 

[Qwertywerty]

1/R = 1/(R_1+R_3) + 1/(R_2+R_4)

Is this wrong?

Well , I'd rather you tried answering that yourself .

When do you use the formula for parallel ( What is a parallel connection ) ?
What is the potential difference between A and B ?

 

[William White]

calculate your TOTAL current

Have two lots of parallel resistors

1&2 R = 1/ (1/R1 + 1/R2)

3&4 = 1/ (1/R3 + 1/R4)

From this, you can work out the total resistance, and the total current.

Once you have the total current, you should be on your way

 

[Qwertywerty]

How do I determine the current in either? Can I use that 1/R = 1/R1 + 1/R2

If you have two resistors in parallel , then current through either will be total current into the ratio of other resistor to total resistance , i.e. , if R_a and R_b are in parallel , i_a = i*R_b/( R_a + R_b ) .

 

[SammyS]

How do I determine the current in either? Can I use that 1/R = 1/R1 + 1/R2


Do you refer to this:

1/R = 1/(R_1+R_3) + 1/(R_2+R_4)

Is this wrong?

Yes, it's wrong.

1/R = 1/(R_1+R_3) + 1/(R_2+R_4 is the result you get if R₁ and R₃ are in series, R₂ and R₄ are in series., and then the two series combinations are in parallel. That would be the case if there was no connection between points A and B.

Why would you use 1/R = 1/R₁ + 1/R₂ ?

(Yes, this is a correct step, but why?)​

 

[meguco0314]

Why would you use 1/R = 1/R₁ + 1/R₂ ?

(Yes, this is a correct step, but why?)​

As you said there are a connection between the two branches. I wasn't sure if R1 and R3 were in series or not because of this, but now I understand.

When I do 1/R = 1/R₁ + 1/R₂ I get that the resistance is 2 Ohm. The resistance for R3 and R4 is 2 Ohm also.

Total resistance for the whole circuit is 2 + 2 = 4 Ohm
Total current = 12 V / 4 Ohm = 3 A

Okay so the total current is 3 A. I have no clue how to go from here.

 

[Qwertywerty]

Okay so the total current is 3 A. I have no clue how to go from here.

If you have two resistors in parallel , then current through either will be total current into the ratio of other resistor to total resistance , i.e. , if Ra and Rb are in parallel , ia = i*Rb/( Ra + Rb ) .

 

[SammyS]

As you said there are a connection between the two branches. I wasn't sure if R1 and R3 were in series or not because of this, but now I understand.

When I do 1/R = 1/R₁ + 1/R₂ I get that the resistance is 2 Ohm. The resistance for R3 and R4 is 2 Ohm also.

Total resistance for the whole circuit is 2 + 2 = 4 Ohm
Total current = 12 V / 4 Ohm = 3 A

Okay so the total current is 3 A. I have no clue how to go from here.

How much voltage is dropped across the R₁ , R₂ combination?

How much voltage is dropped across the R₃ , R₄ combination?

 

[meguco0314]

How much voltage is dropped across the R₁ , R₂ combination?

How much voltage is dropped across the R₃ , R₄ combination?

Both the R₁ , R₂ combination and the R₃ , R₄ combination has 12V, correct?

If so, then according to Qwertywerty


I can use the ratio between R₁ and R₂ and then use that same ratio with the voltage.
So we have a ratio of 2:1. If my theory is correct, the voltage of R₁ should be 4 and R₂ should be 8. Is this correct so far?

 

[SammyS]

Both the R₁ , R₂ combination and the R₃ , R₄ combination has 12V, correct?

Not correct.

You have 3 A passing through 2 Ω in both combinations.

How much voltage is dropped across the R₁ , R₂ combination ?

 

[meguco0314]

You have 3 A passing through 2 Ω in both combinations.

How much voltage is dropped across the R₁ , R₂ combination ?

We have U=R*I and across the R₁ , R₂ combination we have, as you said, 3 A passing through 2 Ω.

The voltage should be 3*2 = 6V in both combinations since the combinations have equal resistance.

Can I figure out the voltage for each resistance now with this information?

 

[SammyS]

We have U=R*I and across the R₁ , R₂ combination we have, as you said, 3 A passing through 2 Ω.

The voltage should be 3*2 = 6V in both combinations since the combinations have equal resistance.

Can I figure out the voltage for each resistance now with this information?

I hope so.

If you know (find) the current through R₁ and the current through R₃, can you get the final answer ?

 

[Qwertywerty]

Can I figure out the voltage for each resistance now with this information?

You should be using the term potential difference / drop instead of voltage ; because voltage doesn't really make sense .

 

[SammyS]

You should be using the term potential difference / drop instead of voltage ; because voltage doesn't really make sense .

Picky - picky !
It's very common usage.

 

[Qwertywerty]

Picky - picky !
It's very common usage.

If you say so . Although I didn't get this -

The voltage should be 3*2 = 6V in both combinations since the combinations have equal resistance.

Can I figure out the voltage for each resistance now with this information?

What voltage is being referred to here ? This seemed a bit confusing as the value 6V had already been found out .

 

[meguco0314]

I hope so.

If you know (find) the current through R₁ and the current through R₃, can you get the final answer ?

Yes I believe so. The difference in current between R₁ and R₃ should be the current that goes through A and B.

I'm not quite sure about the voltage of R₁ and R₃ though. If I understand correctly R₁ has 4V and R₂ has 2V?
R₃ 3V and R₄ 3V.

If this is correct then R₁ has the current 4/3 A and R₃ 3/4 A

 

[SammyS]

If you say so . Although I didn't get this -

Well, the word "voltage" was perfectly OK. However, OP should have included the word "drop" to to make it a "voltage drop" across each resistor.

 

[William White]

You should be using the term potential difference / drop instead of voltage ; because voltage doesn't really make sense .

it makes perfect sense.

dictionary corner
voltage
"an electromotive force or potential difference expressed in volts."


if you were asked to measure the voltage of the supply to your house, would you say that doesn't make sense?


if its good enough for the law
http://www.legislation.gov.uk/uksi/2002/2665/regulation/27/made

 

[SammyS]

I'm not quite sure about the voltage of R₁ and R₃ though. If I understand correctly R₁ has 4V and R₂ has 2V?
R₃ 3V and R₄ 3V.

No those are all incorrect.

What is true for the voltage drop across items which are in parallel ?

 

[Qwertywerty]

it makes perfect sense.

dictionary corner
voltage
"an electromotive force or potential difference expressed in volts."


if you were asked to measure the voltage of the supply to your house, would you say that doesn't make sense?


if its good enough for the law
http://www.legislation.gov.uk/uksi/2002/2665/regulation/27/made

Yeah , got that . Thanks .

 

[meguco0314]

No those are all incorrect.

What is true for the voltage drop across items which are in parallel ?

The voltage is the same for each branch when parallel. But, sorry, I don't know how to go forward from this. The connection between the two branches makes this very complicated for me.

The voltage for R1, R2 combination are 6V. How do I calculate the voltage for R1 and R2 separately? I need the voltage for R1 and R3 in order to calculate their current.

 

[SammyS]

The voltage is the same for each branch when parallel. But, sorry, I don't know how to go forward from this. The connection between the two branches makes this very complicated for me.

The voltage for R1, R2 combination are 6V. How do I calculate the voltage for R1 and R2 separately? I need the voltage for R1 and R3 in order to calculate their current.

For a 6V drop across R₁, how much current must flow through R₁ ?

etc.

 

[Qwertywerty]

Use ΔV = iR for each individual resistor .

 

[meguco0314]

For a 6V drop across R₁, how much current must flow through R₁ ?

etc.

2 A must flow through R₁. And if there is 6V across R₃, 1,5 A must flow through. But since the total current should be 3 A, 0,5 A must go through the AB connection. Correct?

Edit: "But since the total current should be 3 A" I got that wrong I believe in this context. But everything adds up!
2A through R1
0,5A through the AB connection
1A through R2
1,5A through R4

 

[SammyS]

2 A must flow through R₁. And if there is 6V across R₃, 1,5 A must flow through. But since the total current should be 3 A, 0,5 A must go through the AB connection. Correct?

0.5A is correct.

It's the difference of 2A minus 1.5A. The total of 3A has more to do with considering the other two resistors as well.

What direction does the current flow between A & B ?

 

[meguco0314]

0.5A is correct.

It's the difference of 2A minus 1.5A. The total of 3A has more to do with considering the other two resistors as well.

What direction does the current flow between A & B ?

See my edit, I got a bit exited and thought a bit wrong but corrected myself.

Hmm, the direction I am not sure. I think it goes from A to B but I am not sure. How would I know that?

 

[SammyS]

See my edit, I got a bit exited and thought a bit wrong but corrected myself.

Hmm, the direction I am not sure. I think it goes from A to B but I am not sure. How would I know that?

From the direction of current through R₁ and R₃ and the difference in the currents.

Double check all results by considering R₂ & R₄ as well.

 

[meguco0314]

From the direction of current through R₁ and R₃ and the difference in the currents.

Double check all results by considering R₂ & R₄ as well.

Yeah that makes a lot of sense! The direction of the current must be from A to B then.

 

[SammyS]

Yeah that makes a lot of sense! The direction of the current must be from A to B then.

Yes.

 

[William White]

wow, that was exhausting - but well done SammyS, that was an excellent walk though.

 

[SammyS]

wow, that was exhausting - but well done SammyS, that was an excellent walk though.

Thanks.

@Qwertywerty ,

Your suggestions were fine, but I felt that meguco0314 would benefit from using basics rather than using a proportionality argument for finding individual currents.

 

[meguco0314]

Yes thank you so much! Your help was awesome! I learned more than a thing or two from this, and I hope others will benefit from this thread as well. :)