# Circuit analysis potential difference

• hms.tech
In summary, after discussing the potential difference between X and Y and considering the use of KVL and KCL, it was determined that there were two possible answers of 9V and 3V. After further calculations and analysis, it was concluded that the correct answer is 3V using KVL and KCL. The other possible answer of 9V, based on general concepts, was deemed incorrect due to the lack of a series resistor in the circuit.
hms.tech

## Homework Statement

What is the Potential difference between X and Y ?

KVL and KCL

## The Attempt at a Solution

I am confused about the two possible answers :
1. 9V (From general concepts)
2. 3V (after applying the KVL and KCL)

I think the 2nd answer looks correct. Any thoughts ?
Can someone give a description and an explanation for this answer .

#### Attachments

• Untitled.png
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Can you explain the reasoning, or preferably the calculations, behind the two suggested answers? Where did they come from?

gneill said:
Can you explain the reasoning, or preferably the calculations, behind the two suggested answers? Where did they come from?

Ofcourse !

using KVL :

9 - 5$I_{1}$ - 5$I_{2}$ = 0 >>>eq 1
9 - 5$I_{1}$ - 5$I_{3}$ = 0 >>>eq 2
$I_{1}$ = $I_{2}$ + $I_{3}$ >>>eq 3

By comparing eq 1 and eq 2 : $I_{2}$ = $I_{3}$

Now by substitution we find that : $V_{1}$ (voltage across the first resistor the one closest to the 9V rail) = 6 V

This leaves 3 V for the resistors in parallel and hence the terminals X and Y.

Is this reasoning sound for rejecting the answer 9V (across X and Y) and confirming the answer as 3V (across X and Y) ?

hms.tech said:
Ofcourse !

using KVL :

9 - 5$I_{1}$ - 5$I_{2}$ = 0 >>>eq 1
9 - 5$I_{1}$ - 5$I_{3}$ = 0 >>>eq 2
$I_{1}$ = $I_{2}$ + $I_{3}$ >>>eq 3

By comparing eq 1 and eq 2 : $I_{2}$ = $I_{3}$

Now by substitution we find that : $V_{1}$ (voltage across the first resistor the one closest to the 9V rail) = 6 V

This leaves 3 V for the resistors in parallel and hence the terminals X and Y.

Is this reasoning sound for rejecting the answer 9V (across X and Y) and confirming the answer as 3V (across X and Y) ?

Yes, the method is fine and the result, once the stated equations are solved in detail, will give the correct result and allow you to reject the other one.

gneill said:
Yes, the method is fine and the result, once the stated equations are solved in detail, will give the correct result and allow you to reject the other one.

Does that mean my answer is correct ?

(your reply is quite ambiguous )

hms.tech said:
Does that mean my answer is correct ?

(your reply is quite ambiguous )

I didn't see a complete answer... just some (correct) steps along the path to one

gneill said:
I didn't see a complete answer... just some (correct) steps along the path to one

3 V

There is no working left to show (excluding solving the linear equations)

hms.tech said:
3 V

There is no working left to show (excluding solving the linear equations)

All right, so 3 V is correct using KCL and KVL.

Now, what about this "9V (From general concepts)" option? What's the argument for that, and is it good enough to discount the KVL/KCL solution?

gneill said:
All right, so 3 V is correct using KCL and KVL.

Now, what about this "9V (From general concepts)" option? What's the argument for that, and is it good enough to discount the KVL/KCL solution?

I will actually have to upload another circuit to prove my point here

I used this circuit (only a little different than the first) as a reference that if no current flows through the circuit, the p.d across any component is always the same as the e.m.f of the source . Although, given that I worked out the math, I would disregard this flawed concept of mine.

#### Attachments

• Counter ex.png
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Yup. This new circuit lacks the resistance in series with the voltage source, so it's strictly a parallel circuit where all branches have the same potential which is the same as that of the voltage source. The lack of the series resistor is a critical difference.

thank you for the explanation in post no.10
I was looking for something like this

## 1. What is potential difference in circuit analysis?

Potential difference, also known as voltage, is the difference in electrical potential energy between two points in a circuit. It is measured in volts (V) and is essential in understanding the flow of electric current in a circuit.

## 2. How is potential difference calculated?

Potential difference is calculated by dividing the work done by the electric charge by the amount of charge. This can be represented by the equation V = W/Q, where V is the potential difference, W is the work done, and Q is the amount of charge.

## 3. What affects potential difference in a circuit?

Several factors can affect potential difference in a circuit, including the type of material used as a conductor, the length of the conductor, and the temperature of the conductor. Additionally, the presence of resistors and other components can also impact potential difference.

## 4. How does potential difference affect the flow of electric current?

Potential difference is the driving force behind the flow of electric current. The greater the potential difference, the stronger the force pushing the electrons through the circuit. This is why batteries and power sources with higher voltage ratings can produce more current than those with lower ratings.

## 5. Can potential difference be negative?

Yes, potential difference can be negative. This occurs when the direction of the electric current is opposite to the direction of the electric field. In this case, the electric charges are moving from a higher potential to a lower potential, resulting in a negative potential difference.

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