How to find the cell voltage of this circuit?

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Homework Help Overview

The discussion revolves around finding the cell voltage in a circuit involving resistors of various values, specifically focusing on the current through a 15 ohm resistor and its implications for the overall circuit voltage.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the application of Ohm's law and the relationships between current and voltage across different resistors. There are attempts to calculate voltages and currents in series and parallel configurations, with some participants questioning the assumptions about resistor arrangements.

Discussion Status

The discussion has evolved with participants providing guidance on how to approach the problem step by step. There is a recognition of the need to clarify the relationships between different parts of the circuit, and some participants express uncertainty about their calculations, leading to further exploration of the circuit's configuration.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can use or the methods they can apply. There is also a noted confusion regarding the arrangement of resistors and the corresponding voltages, which affects their calculations.

Shadow1999
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Homework Statement


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Find the cell voltage, the current at the 15 OHM resistor is 2A.

Homework Equations


How would I solve to find the cell voltage?

The Attempt at a Solution


I tried to find the voltage of the top part of the circuit but I just cannot remember how you would do that or if it would even result in the solution.
 
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Do you know Ohm's law? Are you familiar with series and parallel connections? Using the given information, what is the voltage across the 15 ohm resistor?
 
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Yes I am familiar with it, the voltage is 30V.
 
Just take it step by step...
If you know the current in the 15 ohm, this will give you the current in the 10 ohm ... from this the current in the 14 ohm ... hence the voltage across all three ... which is the voltage across the 3,4 and 4 ohm ...and so on ...
 
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Shadow1999 said:
Yes I am familiar with it, the voltage is 30V.
Right. So, what is the current through the 10 ohm resistor?
Using that, you can find the voltage across the the network containing 14 ohm, 10 ohm and 15 ohm resistors.
Also, you need to simplify the network of 3 ohm and 4 ohm resistors in order to find the current through it.
 
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cnh1995 said:
Right. So, what is the current through the 10 ohm resistor?
Using that, you can find the voltage across the the network containing 14 ohm, 10 ohm and 15 ohm resistors.
Also, you need to simplify the network of 3 ohm and 4 ohm resistors in order to find the current through it.

The current at 10 ohms would be 3A, I had figured this part out. What I can't figure out is how I would simplify and find the current through the 3 and 4 resistors. The current at 14 OHMS should be 5A?
 
Shadow1999 said:
The current at 14 OHMS should be 5A?
Yes. So, what is the voltage across the 14, 10 and 15 ohm network?
Shadow1999 said:
What I can't figure out is how I would simplify and find the current through the 3 and 4 resistors.
What is the voltage across the 3, 4 and 4 ohm network?
Current through the network would be equal to voltage across the network/equivalent resistance of the network.
What is the equivalent resistance of the 3,4 and 4 ohm network? Can you simplify it using series-parallel reduction technique?
 
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cnh1995 said:
Yes. So, what is the voltage across the 14, 10 and 15 ohm network?

What is the voltage across the 3, 4 and 4 ohm network?
Current through the network would be equal to voltage across the network/equivalent resistance of the network.
What is the equivalent resistance of the 3,4 and 4 ohm network? Can you simplify it using series-parallel reduction technique?

I don't know how to find the voltage across the 3, 4 and 4 ohm network.
The equivalent resistance of 3,4 and 4 ohms should be 5 ohms?
 
Shadow1999 said:
The equivalent resistance of 3,4 and 4 ohms should be 5 ohms?
Yes.
Shadow1999 said:
I don't know how to find the voltage
oz93666 said:
Just take it step by step...
If you know the current in the 15 ohm, this will give you the current in the 10 ohm ... from this the current in the 14 ohm ... hence the voltage across all three ... which is the voltage across the 3,4 and 4 ohm ...and so on ...
 
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  • #10
cnh1995 said:
Yes.

Okay so the voltage at the 14 OHMS should be 70V (V=IR) 70=(14)(5). From what I know, 3 OHMS and 14 OHMS are parallel so they'll have the same voltage? Therefore 70/3 should be 23.3A, that's the total current across the 3,4 and 4 ohm network? So 23.3A + 5A = 28.3A. Next to find the total cell voltage I do V=(28.3)(9) which equals to 255V. Now something in my work there is wrong as the correct answer in my textbook is 225V. I've tried to figure out what I did incorrect but I just can't seem to put a finger on it. It's now 4am and I've been on this single question for over an hour.
 
  • #11
Shadow1999 said:
3 OHMS and 14 OHMS are parallel
They are not.
Shadow1999 said:
Okay so the voltage at the 14 OHMS should be 70V (V=IR) 70=(14)(5).
Right. So what is the voltage across the "entire network of 14, 10 and 15 ohm resistors"?
That will also be the voltage across the "entire network" of 3, 3 and 4 ohm resistors since these two "networks" are in parallel and not individual resistors.
Shadow1999 said:
the correct answer in my textbook is 225V.
I am getting the same answer.
 
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  • #12
cnh1995 said:
They are not.

Right. So what is the voltage across the "entire network of 14, 10 and 15 ohm resistors"?
That will also be the voltage across the "entire network" of 3, 3 and 4 ohm resistors since these two "networks" are in parallel and not individual resistors.

I am getting the same answer.

Shouldn't the voltage across that entire network be equal to 70V as well?
 
  • #13
Shadow1999 said:
Shouldn't the voltage across that entire network be equal to 70V as well?
What about the voltage across the 15 ohm resistor you calculated earlier?
 
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  • #14
cnh1995 said:
What about the voltage across the 15 ohm resistor you calculated earlier?
cnh1995 said:
What about the voltage across the 15 ohm resistor you calculated earlier?

70+30=100 Is it 100V?
 
  • #15
Shadow1999 said:
70+30=100 Is it 100V?
Yes.
 
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  • #16
cnh1995 said:
Yes.

I understand, I had previously thought that the 15 and 10 OHM resistor had the same voltage as 14 OHMS but I was wrong. I understand that you need to find the total resistance which is 100 across the whole network. Then you divide 100 on the bottom by 20 OHMS and the top network you divide the 100 by 5 ohms which gives you a total of 25A. V=(25)(9) --> V=225v

Thank you so much for your help, you really helped me understand the concept I owe you one!
 
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  • #17
Shadow1999 said:
I understand, I had previously thought that the 15 and 10 OHM resistor had the same voltage as 14 OHMS but I was wrong. I understand that you need to find the total resistance which is 100 across the whole network. Then you divide 100 on the bottom by 20 OHMS and the top network you divide the 100 by 5 ohms which gives you a total of 25A. V=(25)(9) --> V=225v
Right.
You can also solve it by inspection only. Current through the lower network is 5A and voltage across both the networks is 100V. Knowing the equivalent resistance of the upper network as 5 ohm, current through the upper network will be 100/5=20A.
So, total current will be 25A which is nothing but the current through the 5 ohm resistor on the left. So, voltage across that 5 ohm resistor is 125V. So the cell voltage will be 125+100=225V.
Shadow1999 said:
Thank you so much for your help, you really helped me understand the concept I owe you one!
You are welcome!:smile:
 
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