# 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

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 .

• meguco0314
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 ?

Last edited:
William White

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 Ra and Rb are in parallel , ia = i*Rb/( Ra + Rb ) .

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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 ) .

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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?

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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?

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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 .

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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

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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

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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
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.

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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.

• meguco0314
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

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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
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?

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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
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.

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

• meguco0314 and William White
William White
wow, that was exhausting - but well done SammyS, that was an excellent walk though.

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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.

• Qwertywerty and meguco0314
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. :)