All About the Derivation of Electric Potential Difference

Electric potential difference is the electrical force, measured in volts, that drives current through a circuit. Talking about the derivation of electric potential difference, the electric potential difference between two points can be derived from the work done by a force moving a charge from one point to another. This work is equal to the product of the charge and the electric potential difference between the points.

The Concept of Electric Potential Difference

The voltage of a battery, for example, is determined by the number of charged particles it has available to create a potential difference. For electrons to flow from the battery’s negative terminal to the positive terminal, a conductor must be placed between them. This conductor allows electrons to move freely through it as they flow from high to low potential. The movement of these charged particles creates an electrical current that powers the various systems and devices. 

The Derivation of Electric Potential Difference

Isn’t holding a hot cup of coffee on the cold winter mornings bliss? Have you ever wondered how you can feel the heat of the cup in your cold hands in just a moment? This is because of the flow of heat. The heat flows from a high temperature to a lower temperature. Taking another example where water flows from a higher point to the lower, this is how the waterfalls work. 

Similarly, when we talk about the electric potential difference, the voltage also flows from a higher point to a lower one. In simple terms, the charge flows from a higher to a lower potential. The potential difference between the two charges is different, one is higher and the other is lower, just as in the above case of heat and water.

The potential between any two points cannot be the same because there will be no current flow. Again, the heat will not flow between the two bodies with the same temperatures; the water will only flow from a higher height to the lower and not between the two same points (heights). Thus, the two charges must have different potentials.

Derivation:

Suppose there are two bodies, say A and B. A possesses +Q, the positive unit charge that flows to body B. While the charge flows from A to B, some work is done. This work done while replacing +Q from A to B is known as the POTENTIAL DIFFERENCE. 

Mathematically,

Potential Difference can be denoted as ΔV (Voltage)

The Charge is denoted as Q

Total work done in moving Q from A to B can be denoted as ‘Q.’

Therefore,

The formula is,

ΔV = W/Q

Potential Difference = Work done upon the unit of positive charge

The SI unit of work is Joule (J)

The unit of charge is Coulomb (C)

Thus,

Volt = J/C

Now, ΔV= final voltage – initial voltage,

I.e. VB-VA 

Work done= Work done from A to B,

I.e. WA 🡪B

The equation for electric potential difference becomes 

VB-VA = WA 🡪 B/Q………. Equation 1

This gives the following final formula of potential difference:

ΔV = W/Q

The equation for electric potential is:

ΔV= VB-V∞ = W∞ 🡪 B/Q……….. Equation 2

Equation 2 represents the electric potential, i.e. determines the work done (total external) when a charge is brought from infinity to another point. 

An overview of the SI unit of electric potential difference

Why  is V used to represent the electric potential difference?

V stands for Volt, the SI unit of electric potential difference.

The volt (symbol: V) is the SI unit of electric potential difference and electromotive force. Volt is named after Alessandro Volta, an Italian physicist who invented the first electric battery. The volt is equivalent to joule per coulomb and is defined as the potential difference between two points of a conductor when an electric current of one ampere dissipates one watt of power between those points.

Factors Affecting the Potential Difference

Nowadays, potential difference and electric current are used everywhere. We use it in our homes, workplaces and schools. We use it to power lights, refrigerators and other appliances. It is used to run different systems and machines. But on what factors does the potential difference depend? 

The potential difference between two points in a circuit is determined by the following factors: the resistance of the wire, the number of cells in the battery and the distance between the points. All of these factors must be taken into account when calculating the potential difference. If any one of these factors is changed, then so will the potential difference.

Calculation of Voltage using Ohm’s Law:

V=IR

V= Voltage

I=Current

R= Resistance

Conclusion

Electric potential difference calculation is a process by which the work done to move a unit positive charge from one point to another in an electric field is determined. This quantity, denoted by voltage or potential difference, is measured in volts. Therefore, the electric potential difference is responsible for powering all electrical devices and systems, making it an essential aspect of our everyday lives.