# Potential difference across two points in a circuit

• plazprestige
In summary, the potential difference between points b and a in the given circuit is -13 V. This was found by first using Kirchhoff's voltage law to solve for the voltages of the two batteries in the circuit, and then applying the concept of potential difference to find the change in potential from point a to point b. It is important to note that the potential difference between two points can be calculated in either direction, but it is crucial to follow the specified direction in the question to determine the correct sign of the potential difference.

## Homework Statement

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Find the potential difference between points b and a in the circuit below

I have already solved for the voltages of the two batteries (1 and 2) in the circuit (18 V and 7 V respectively)

2. Homework Equations

Kirchhoff's Rules
1) Potential difference across any closed loop is 0
2) Current in = current out

## The Attempt at a Solution

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I have read that Kirchhoff's current rule is how to approach these kinds of problems, but I am not sure how.

You have found the voltages of the batteries correctly. How did you do it? For that, you had to use the potential difference between points a and b, that you know from the uppermost branch of the circuit.

I used Kirchhoffs voltage law to find the battery voltages. Could you elaborate on how I unknowingly found the potential difference between b and a please?

plazprestige said:
I used Kirchhoffs voltage law to find the battery voltages. Could you elaborate on how I unknowingly found the potential difference between b and a please?

For battery 2:

-2(1) - E2 - 2(2) - 1(6) + 20 -1(1) = 0, solve for E2 (Kirchhoff's voltage law around the large loop)

For battery 1:

E1 - 1(1) - 1(4) - 2(1) - E2 - 2(2) = 0, solve for E1 (Kirchhoff's voltage law around the bottom half loop)

plazprestige said:
For battery 2:

-2(1) - E2 - 2(2) - 1(6) + 20 -1(1) = 0, solve for E2 (Kirchhoff's voltage law around the large loop)

You started from point a and and followed the change of potential along the current. The potential change from a to b is Ub-Ua = -2(1) - E2 - 2(2) .
From b to a, to potential changes by - 1(6) + 20 -1(1)= Ua-Ub. The potential difference between b and a is Ub-Ua = ? :)

ehild said:
You started from point a and and followed the change of potential along the current. The potential change from a to b is Ub-Ua = -2(1) - E2 - 2(2) .
From b to a, to potential changes by - 1(6) + 20 -1(1)= Ua-Ub. The potential difference between b and a is Ub-Ua = ? :)

Oh, I think I understand. So if I start at point b and end at point a:

-1(6) + 20 - 1(1) = Vb - Va = 13 V

Is this correct? I only I have one try left, so I don't want to squander it.

It must be correct.

Ok, I got the magnitude right (13) but the sign wrong (it was - 13 V). I don't understand why. If it wanted the potential difference from b to a, why would you not start at b and work your way towards a?

It depends how the potential difference between points a and b is defined. Usually it is Ua-Ub. But the question was the potential between b and a, which is Ub-Ua, and it is negative.

Could you explain how to get the sign right? I don't understand why it's negative rather than positive.

plazprestige said:
Could you explain how to get the sign right? I don't understand why it's negative rather than positive.

In Post #6, the potential changed from Vb to Va by 13 V. So Va =13+ Vb, Va-Vb =13 . When it is said "potential difference between X and Y" your book means that you have to take the change of potential from Y to X: VX-VY.
The question was
Find the potential difference between points b and a in the circuit below

You have to find the potential at b with respect to a, that is, Vb-Va. Vb-Va = - (Va-Vb) = -13 V

## 1. What is potential difference and how is it measured?

Potential difference, also known as voltage, is the difference in electric potential between two points in a circuit. It is measured in volts (V) using a voltmeter.

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

Potential difference is what drives the flow of electric current through a circuit. The higher the potential difference, the greater the force pushing the electric charges to move.

## 3. What factors can affect the potential difference in a circuit?

The potential difference in a circuit can be affected by the type of power source, the resistance of the circuit components, and the configuration of the circuit (e.g. series or parallel).

## 4. 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, resulting in a decrease in potential as the charges move through the circuit.

## 5. How is potential difference related to energy?

Potential difference is directly related to the amount of energy transferred in a circuit. The higher the potential difference, the more energy is transferred per unit of charge, resulting in a greater amount of work being done by the electric current.