Help in solving an electricity circuit problem involving Kirchoff's law

[Eobardrush]

Homework Statement

Calculate EMF of E1

Relevant Equations

V=IR
E=IR1+IR2
I=I1+I2

My initial solving method was taking 1.75A and adding the resistors at the 1st loop(4 and 8 ohms) to get the answer

V=IR
V=1.75(4+8)
V=21V

But the answer sheet uses 0.75A instead of 1.75A to find EMF of E1.

So according to the answer sheet its
V=0.75(4+8)
V=9V

0.75A is the answer for the i) question. And I am confused as to why use 0.75 instead of 1.75. Isn't 1.75A the current transferred by the E1 battery since its even coming from the direction of E1?

 

[collinsmark]

Homework Statement:: Calculate EMF of E1
Relevant Equations:: V=IR
E=IR1+IR2
I=I1+I2

View attachment 295223

My initial solving method was taking 1.75A and adding the resistors at the 1st loop(4 and 8 ohms) to get the answer

V=IR
V=1.75(4+8)
V=21V

But the answer sheet uses 0.75A instead of 1.75A to find EMF of E1.

There might be a couple of missteps you made there.

But let's start from the basics. What is Kirchhoff's first law? (Hint: it doesn't have anything to do with voltage. So the fact that you jumped into using voltage from the get-go is perhaps the main misstep.)

So according to the answer sheet its
V=0.75(4+8)
V=9V

0.75A is the answer for the i) question. And I am confused as to why use 0.75 instead of 1.75. Isn't 1.75A the current transferred by the E1 battery since its even coming from the direction of E1?

The answer sheet is correct. This should be more obvious after you've solved part i.

 

[Eobardrush]

There might be a couple of missteps you made there.

But let's start from the basics. What is Kirchhoff's first law? (Hint: it doesn't have anything to do with voltage. So the fact that you jumped into using voltage from the get-go is perhaps the main misstep.)
The answer sheet is correct. This should be more obvious after you've solved part i.

Isn't the first law about currents dividing. Basically I1=I2+I3

But since we are finding the EMF of the battery, shouldn't we use the total current, therefore I1?

In other words shouldn't the current BEFORE it splits be the actual current transferred by the battery E1?
That is the reason why I did not use 0.75 since that is the current after the total current was divided

 

[cnh1995]

That is the reason why I did not use 0.75 since that is the current after the total current was divided

If you apply Kirchhoff's voltage law in the upper loop (which you need to do to find the emf E1), which current shows up in the equation?

 

[collinsmark]

Isn't the first law about currents dividing. Basically I1=I2+I3

But since we are finding the EMF of the battery, shouldn't we use the total current, therefore I1?

In other words shouldn't the current BEFORE it splits be the actual current transferred by the battery E1?
That is the reason why I did not use 0.75 since that is the current after the total current was divided

Kirchhoff's first law states that the sum of currents meeting at a point is zero.

Look at the left part of the figure. There are three arrows present, and two of them are labeled with known currents. Using Kirchhoff's first law, find the current in the third. (And pay attention to the arrows, or at least the directions of the currents, if you want to define your own arrows. The directions of the currents are important in this step, whether that's based on the given arrows or your own arrows.)

 

[Steve4Physics]

Hi @Eobardrush. I'm guessing you are struggling with some of the basics. See if this helps,

The 4Ω and the 8Ω resistors are in series, so I don’t think I’m giving too much away when I say you can replace them by a new single 12Ω resistor.

You can now work through these questions:
a) What current passes through the (new) 12Ω resistor? Explain.
b) Using your answer to part a), what is the voltage across the (new) 12Ω resistor? Explain.
c) Using your answer to part b), what is E1? Explain.

 

[Eobardrush]

Hi @Eobardrush. I'm guessing you are struggling with some of the basics. See if this helps,

The 4Ω and the 8Ω resistors are in series, so I don’t think I’m giving too much away when I say you can replace them by a new single 12Ω resistor.

You can now work through these questions:
a) What current passes through the (new) 12Ω resistor? Explain.
b) Using your answer to part a), what is the voltage across the (new) 12Ω resistor? Explain.
c) Using your answer to part b), what is E1? Explain.

Actually I do understand question A and B here. But I am struggling to understand why there is a 1.75A in the diagram. Is that maybe the combined current for E2 and E1? If so then I think I understand.

The reason I was struggling is that I am not 100% sure if 1.75A is just the current for E1 or the combination of both E1 and E2

The fact that the diagram shows an arrow coming from E1 as 1.75A makes it look like its the actual total current from E1 so its making it a bit confusing

And sorry I know I am really dumb. Been self teaching myself actually

 

[Steve4Physics]

Actually I do understand question A and B here.

You have not given answers, so there is no way of telling if you have a correct understanding or not.

But I am struggling to understand why there is a 1.75A

The cell is ideal (a fixed emf and zero internal resistance). That means the cell can deliver any current (e.g. 0.000001A or 1000000A) depending on what’s in the rest of the circuit. As a consequence, knowing the current through the cell (1.75A) does not directly help you to find the cell’s emf.

I suggest you read the next paragraph carefully and then go back to the Post #6 questions.

An ideal cell’s emf is always equal to the voltage between the its terminals. Using this fact, and the answers to Post #6 questions a) and b) let's you find E1.