Potential Difference: Principle and Applications

Potential difference is the difference in electric potential between two points. For example, if we take a copper wire, electricity will not flow through it until it is triggered by a potential difference between the two points of the wire. When two negative (-) charges are brought close together, they repel each other due to strong electric potential (a type of potential energy); similarly, when two positive charges (+) are brought together, they repel each other. When a negative (-) and positive (+) charge are brought nearer, they attract one another, allowing a current to flow. This flow of current is due to the potential difference between the two charges. 

The SI unit of potential difference is “volt” (V), named after the Italian physicist Alessandro Volta and is measured using an instrument called a voltmeter. When an electric current of one ampere dissipates one watt of power between two points of a conducting wire, the electric potential between those points is considered to be one volt. The dimensional formula of potential difference is [M1 L2 T-3 I-1].

Dimension of Potential Difference

The dimension formula for any quantity is the representation that describes the powers to which the fundamental units are raised to get one unit of a derived quantity. It is mostly used to derive relationships between physical quantities, convert one system of units to another and check the accuracy of an equation. 

When calculating dimensional formulas, the base dimensions considered are mass, time, temperature, length and current. Metre, second, ampere, mole, kilogramme, kelvin and candela are taken as fundamental units.

As discussed above, the dimension formula for potential difference is given as [M1 L2 T-3 I-1], where, 

• M = Mass in kilogrammes

• L = Length of the wire

• T = Time in seconds

• I = Current in amperes

Let us see how the dimension of potential difference is derived using base dimensions and fundamental units. 

The potential difference or voltage, is defined as the amount of external work necessary to transfer a charge from one place to another in an electric field. It can be written as 

Potential difference = work done × [charge]-1 ….. (1)

Since work done = force (m × a) × displacement ….. (2)

The dimensional formula for mass, displacement, and acceleration can be written as:

Mass = [M1 L0 T0] ….. (3)

Displacement = [M0 L1 T0] ….. (4)

Acceleration = [M0 L1 T-2] ….. (5)

After substituting equations (3), (4) and (5) in equation (2), we get,

Work done = [M1 L0 T0] × [M0 L1 T-2] × [M0 L1 T0]

Therefore dimensions for work done = [M1 L2 T-2] ….. (6)

We know that charge = current × time and we can write it as:

Charge = [M0 L0 T1 I1] ….. (7)

Now substitute equation (6) and (7) into (1), we get

Potential difference = [M1 L2 T-2] × [M0 L0 T1 I1] = [M1 L2 T-3 I-1] 

Therefore, the dimension of potential difference is represented as [M1 L2 T-3 I-1] 

Difference Between Electric Potential and Potential Difference

The electric potential of any charged body describes how much stored energy it has. It is defined as the amount of work required per unit charge to move a charge from infinity to a point in the electric field. The body saves this work in the form of electric potential. The work can be done by the charged entity exerting a repulsive or attractive force on the other charged particles.

Electric potential = Work done/ Charge =W/Q

Here, the work is measured in joules and charge is measured in coulombs. Hence, the unit for electric potential is joules/coulombs or volts.  

Potential difference is the difference in the electric potential of the two charged bodies. In simple terms, it is the potential developed while performing work to transport a unit charge in coulombs from one point to another in an electric field. Potential difference is measured in joules/coulombs or volts.

Application of Potential Difference

All electrical gadgets use the principle of potential difference in their electric circuits. This potential difference can be used to figure out how much energy is available to push the charges around the circuit. 

The electrical circuits involve the movement of charges between different locations within the electric field. Because a charge with a greater potential has more potential energy and a charge with a lower potential has less, work must be done to shift the charge from the higher potential to the lower potential. 

Electrical appliances either work on direct current (DC) or alternating current (AC). In direct current, the charge flows in one direction, but in alternating current, the charge changes direction on a regular basis. Electrical instruments like mobiles and solar cells work on DC, whereas appliances, such as air-conditioners, generators, or refrigerators, work on AC.

Conclusion

This chapter includes in-depth notes on potential differences and its applications. It addresses the dimension of potential difference and proves the formula in a step-by-step process. The article also explains the difference between electric potential and potential difference.