# Figuring out when to use the two different voltage equations

In summary, the conversation discusses two problems involving electric potential and electric field. In the first problem, we use the equation ΔV=U/q to find the electric field, while in the second problem, we use the equation ΔV=-Ed to find the electric potential energy. The reason for the difference in signs is due to the direction of the electric field lines, which point from high potential to low potential. In the first problem, there is no movement of charges, while in the second problem, there is movement against the electric field lines.

## Homework Statement

I have two problems, both using different equations for electric potential. Confused on when to use which.
First problem:
Two parallel plates connected by a battery whose electric potential is 12V. One plate Has charge density σ+ and the other has Charge density σ+. The plates are spaced 3x10-3m. We want to find the electric field. The way the problem is solved:
ΔV=U/q
U=qEd
Combining the two above:
ΔV=Ed→E=ΔV/d→E=12V/(3x10-3m)=4x103V

The next problem wants to know the electric potential energy of moving a proton like the attached picture.
It is solved like this:
ΔV=-Ed=-(8x104V/m)(0.5m)=-4x104V
Then:
ΔU=qΔV=(1.602x10-19C)(-4x104V)=-6.4x10-15J

My question:
Why I’m the first problem did we say ΔV=Ed
And in the second problem
ΔV=-Ed?
Thanks!

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The Greek letter Δ stands for "change" of the quantity that follows. Change is defined as final value minus initial value, what comes later minus what comes earlier. Electric field lines always point from a region of high potential V to a region of low potential V. So, if you move with the field lines, the change is negative and if you move against the field lines, the change is positive.

In the first question you are given the "voltage" or electric potential difference across the battery terminals. This is conventionally chosen as positive. In this problem there is no movement of charges from one terminal to the other as is the case in the second problem.

kuruman said:
The Greek letter Δ stands for "change" of the quantity that follows. Change is defined as final value minus initial value, what comes later minus what comes earlier. Electric field lines always point from a region of high potential V to a region of low potential V. So, if you move with the field lines, the change is negative and if you move against the field lines, the change is positive.

In the first question you are given the "voltage" or electric potential difference across the battery terminals. This is conventionally chosen as positive. In this problem there is no movement of charges from one terminal to the other as is the case in the second problem.
Thank you! I didn’t know that about electric field lines.

## 1. How do I know when to use the voltage equation V=IR versus V=Ed?

The V=IR equation is used to calculate the voltage drop across a resistor in a series circuit, where V is the voltage, I is the current, and R is the resistance. The V=Ed equation is used in parallel circuits to calculate the voltage drop across a component, where V is the voltage, E is the electromotive force, and d is the distance between the two points. So, the equation you use depends on the type of circuit and the information you have about it.

## 2. Can I use either voltage equation for any circuit?

No, each voltage equation is specific to its type of circuit. The V=IR equation is used for series circuits, while the V=Ed equation is used for parallel circuits. It is important to correctly identify the type of circuit you are dealing with in order to use the correct voltage equation.

## 3. What is the difference between the two voltage equations?

The main difference between the two voltage equations is the type of circuit they are used for. The V=IR equation is used for series circuits, where components are connected one after the other in a single loop. The V=Ed equation is used for parallel circuits, where components are connected side by side on separate branches.

## 4. How do I know which voltage equation to use for a specific circuit?

To determine which voltage equation to use, you need to first identify the type of circuit. If the components are connected in a single loop, it is a series circuit and you should use the V=IR equation. If the components are connected side by side on separate branches, it is a parallel circuit and you should use the V=Ed equation.

## 5. Can I use both voltage equations in the same circuit?

It is not common to use both voltage equations in the same circuit, as this would indicate a more complex circuit. However, it is possible to use both equations if the circuit has both series and parallel components. In this case, you would need to use the appropriate equation for each component or section of the circuit.

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