# Voltage Law & Work: Get Your Misconceptions Straight

• JFS321
In summary: When current is flowing in both directions (like when you have a light switch on and off) then the voltage drop (potential energy) is not the same. In summary, the Voltage Law states that if you have a potential difference (voltage) between two points, the total voltage will be the sum of the voltages at each point.

#### JFS321

Hi all, I'll continue on my quest to get my misconceptions straight. I appreciate the help so far.

Let me explain my thinking about the Voltage Law and please identify where I might be going wrong.

I've been reading as much as possible on voltage drop and how it relates to work. Let's take an example battery of 10V. At the end of the circuit, voltage drops to zero of course.

A) Is this voltage drop equivalent to the work done by the circuit...or is work ONLY done by the battery to raise 0V back up to 10V?

B) I realize that charges flowing "downhill" much like a bowling ball dropped off a mountain eventually return to zero volts with zero potential energy. But, I'm fuzzy on what intuitively causes this change in a battery loop. Is the voltage drop in this case due to the inherent loss voltage as current encounters wire resistance, or is this the loss simply because current is reaching the negative terminal and thus no longer traveling toward a potential difference?

C) Also, similar to A, I am confused on whether or not work is only considered "work" if it opposes the current flow. Meaning, resistors/bulbs/etc. do work because they cause a voltage drop by opposing the direction of current.

THANKS to all...I can't wait to get this straight!

Do you know what the definition of "work" is in physics?

W = Force x distance; in the case of voltage it is W = q x delta V. In this form, I'm not quite sure how distance is included.

I don't know if this will help you at all, but remember that voltage is relative. When you say the potential is zero, it is zero relative to your ground. This is analogous to gravitational potential energy. If you say that potential energy is zero at the surface of the earth, it it relative and only zero because you established zero to be at the surface of the earth.

It might be helpful to think of electrical potential in terms of charges, rather than circuits. Take a lone electron in the universe, and there is a potential associated with that charge. Now, imagine taking another electron at infinity and bringing it to that first electron. It takes mechanical work to move it against the electric force. The potential at all points in the universe is now twice the magnitude and you can establish infinity as the zero potential point.

In circuits we don't typically say zero potential is at infinity. It is more practical to establish one point in the circuit as the ground.

@JFS321
If a battery is 'ideal' then it will always produce the same output voltage V. That means that every Coulomb of Charge that flows from + to - terminal will dissipate V Joules of energy. If you connect a short circuit (just some copper wire) then a lot of current will flow so a lot of energy will be supplied from the battery and the wire will get very hot.

The Dropped Bowling Ball model is the equivalent of connecting a copper wire from the + terminal and having a very short length of resistance wire near the - terminal. All the energy is dissipated right at the 'bottom' terminal. This is just like the dropped ball which only dissipates its energy when it hits the bottom.
If you attached the heavy ball to a rope and pulley with a brake, you would be dissipating the (same mgh) energy steadily as it fell - just like having a long length of resistance wire with the same value as the short bit in the first example.

Hello JFS.. I am really concerned about your language, it seems to go around the topic but in no case hit any thing 100% correct.

Voltage Law -- While this derives from the conservation of energy, the thinking has nothing to do with energy. In short "the sum of voltages (potential differences) around a circuit will sum to Zero" ( ALWAYS!) . Voltage on it's own has effectively nothing to do with energy(the ability to do work)... a small battery at 1.5 V has much more stored energy than your body when you scuff your feet and build up a static charge - which can literately be 10,000 V.

So going around a circuit with an ideal 10V Battery and three 1 Ohm resistors in series has exactly the voltage drops as 10V Battery and three 1,000 Ohm Resistors. - in both cases each resistor has 3.33333... V --- but the 1 ohm case is converting much more electrical energy to heat ( for the PF literalists here it first converts chemical energy to electrical and then to heat).

As for B... this Voltage law -- really does not require the classical complete circuit. If you have a battery and 2 resistors and then remove one resistor - leaving a gap... all of the potential will be across the open circuit. ( Battery +10V, Resistor 0V and Open Gap -10V = 0 V around the loop).

Last one ... think about the meaning of Work. When you charge a battery you are storing energy and doing work... when the battery lights a light bulb it is doing work... work is the movement of energy - energy is not created or destroyed... we just play with it...

Voltage on it's own has effectively nothing to do with energy(
An I am "concerned" about what you write, too. How do you justify this statement when the definition of One Volt is One Joule per Coulomb? Arm waving and random numerical examples can't take us away from that simple energy based definition.

By Joule(energy) per unit Charge - we are back to only a potential(essentially a force)... and not a true measure of energy. In short - Voltage is not a measure of energy. V * C is - without the Coulombs - you can not discuss energy...thus the part of my comment "on it's own"... If you can demonstrate how my "arm waving" is not numerically accurate - then please do so.

By Joule(energy) per unit Charge - we are back to only a potential(essentially a force)... and not a true measure of energy. In short - Voltage is not a measure of energy. V * C is - without the Coulombs - you can not discuss energy...thus the part of my comment "on it's own"... If you can demonstrate how my "arm waving" is not numerically accurate - then please do so.

I assume your numerical examples are accurate, of course but one of the first things that a Scientist tries to do is to throw numbers away and use symbols - to avoid loss of generality. By arm waving, I mean not using the accepted definitions of terms and using your own alternatives.
You need to go back to basics. Voltage is not a force ('emf' is a misnomer and it's a term that is only used as an exception to the rule).
Colloquially, the word 'Volts' is used in stead of Potential Difference. I can't think anyone would associate Gravitational Potential directly with force; just as with Electrical Potential, it relates to the energy / work done in moving a unit mass / charge.
I guess the clincher in this argument is that Voltage (potential difference) is a Scalar quantity and Force is a Vector quantity. They really can't be synonymous. Field is the gradient of Potential. nd Field is Force per unit mass / charge.

Sophie.. I certainly do not mean to challenge your authority here. We should be trying to show how EE is simple, not a point of debate! I want to educate and pull interested people into understanding. There are many ways to understand ...

EE is not simple and it does no one any favours to try to kid them that it is. The purpose of PF ( and you can read the statements in the Global Guidelines, which you can access via the Info button at the top) is to maintain a high standard of discussion, along professional lines. It is not 'professional' to say that an Analogue quantity is the same as a Vector. It is not professional to imply that Potential is not based on Energy. There are dozens of Forums where arm waving is quite acceptable and it's possible to have fun on those forums, saying more or less anything you want. I don't think there is any point in debasing the general high standard of PF by giving inaccurate ideas and information.
If you want people to understand EE then you have to tell them the correct information - surely? That is not being pedantic; it is being helpful.

sophiecentaur said:
By arm waving, I mean not using the accepted definitions of terms and using your own alternatives.
You need to go back to basics.

Vocabulary is the first step
precision in expressing thoughts is next

OP needs to work on both
because
A question well stated is half answered...

Do you understand what is
work
energy
charge
electric field
absolute potential
potential diffference
coulomb
ampere
joule
volt
watt
watt-second

These basic concepts are necessary to become good at circuits.

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sophiecentaur

## 1. What is the voltage law and how does it work?

The voltage law, also known as Kirchhoff's Voltage Law (KVL), states that the sum of all voltages in a closed loop in a circuit must equal zero. This means that as electrical charges move through a circuit, the voltage changes they experience must balance out to zero by the time they return to their starting point. KVL is based on the principle of conservation of energy, where the energy used to overcome resistances in a circuit must equal the energy supplied by the voltage sources.

## 2. What are some common misconceptions about voltage law?

One common misconception is that KVL only applies to series circuits. In reality, it applies to all types of circuits, including parallel and complex circuits. Another misconception is that the voltage drops across all elements in a series circuit must be equal. While this may be true in some cases, it is not a requirement for KVL to hold.

## 3. How does voltage law relate to Ohm's law?

Ohm's law states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance. This law is based on the fundamental relationship between voltage, current, and resistance. KVL, on the other hand, is a general principle that applies to all types of circuits and is based on the principle of conservation of energy.

## 4. Can voltage law be applied to alternating current (AC) circuits?

Yes, voltage law can be applied to both DC and AC circuits. However, in AC circuits, the voltage and current values are constantly changing, so the application of KVL becomes more complex. It is usually easier to apply KVL to AC circuits using phasor diagrams or complex numbers.

## 5. How can I use voltage law to analyze and solve circuit problems?

To use voltage law in circuit analysis, you need to first identify all the closed loops in the circuit. Then, starting at any point in the loop, assign a direction to the current flow and apply the signs (+/-) to the voltage values in the loop according to the direction of the current. Next, write out the KVL equation by summing up all the voltage values in the loop and setting them equal to zero. From there, you can solve for any unknown voltages in the circuit. It is helpful to draw a circuit diagram and label the voltage and current values to keep track of the signs and directions as you work through the equations.