Dimensions of Potential Difference

Potential difference plays a crucial role in the flow of electric current. The definition of electric potential states that the amount of work required to move a positive unit charge from infinity to a point is the potential of that point. When there is a difference between the potential of two points, a potential gradient is formed, which allows current to flow.

What is Potential Difference?

Potential difference refers to the amount of work required to move a unit charge from one point to another. One point will have a higher potential, while the other will have a lower potential. Work must be done when moving a positive charge from a point of lower potential to a point of higher potential.

Unit of Potential Difference

The unit of potential difference is the volt (V). One volt is defined as the potential difference between two points in a circuit when one joule of energy is used to move one coulomb of charge between those two points.

Mathematically, it is expressed as:

1 V = 1 Joule / 1 Coulomb

This relationship illustrates that a potential difference of 1 volt exists when 1 joule of work is done to move 1 coulomb of charge between two points in an electric field.

Potential difference as a scalar quantity

Potential difference is considered a scalar quantity because it only has magnitude and no directional property. Unlike vector quantities, which require both magnitude and direction (like force or velocity), potential difference is concerned solely with the difference in electric potential energy between two points, and it does not involve any inherent directionality.

In an electric circuit, potential difference tells us how much energy per charge is being used or provided, but it doesn’t need a directional component to describe this; it simply measures the difference in energy levels (in volts) across two points. Therefore, it can be added or subtracted directly without considering direction, making it scalar by nature.

Dimensional Formula of Potential Difference

From the definition discussed above, the potential difference can be written as :

ΔV= Δ W/Q

Q = electric charge

W = work done

So, dimension of potential difference= dimension of work done / dimension of electric charge.

W= F.S

So, dimension of W = [MLT_-2] x [L] = [ML₂T_-2]

So, dimension of ΔV = [ML₂T_-2] / [IT] = [MI_-1L₂T_-3]

So, the dimension of potential difference is [MI-1L2T-3]

Potential Difference and EMF of a Cell

The potential difference between the electrodes of a Galvanic cell is called the cell potential. It is defined as the difference between the reduction potentials of the anode and cathode, measured in volts.

When no current is drawn from the cell, the potential difference is termed the EMF (electromotive force). The EMF is positive and is calculated as the difference between the potentials of the half-cell on the right and the half-cell on the left.

EMF Formula:

Ecell = Eright – Eleft ….. (eq1)

Cell Reaction:

In this example, the copper electrode acts as the anode, and the silver electrode is the cathode. The overall reaction is:

Cu (s) + 2Ag+ (aq) → Cu2+ (aq) + 2 Ag (s) ……. (eq2)

Here, (s) indicates the solid state of the electrode, and (aq) represents the ions dissolved in water.

Half-cell reactions

• Cathode (reduction): 2Ag⁺(aq)+2e⁻→2Ag(s)
• Anode (oxidation): Cu(s)→Cu²⁺(aq)+2e⁻

The overall cell reaction is the summation of these two half-cell reactions.

Difference between Cell Potential and EMF

FAQs on Dimensions of Potential Difference

.” image-0=”” headline-1=”h3″ question-1=”What is the dimension of PE?” answer-1=”The dimensional formula of Potential Energy (PE) is [ML²T⁻²], which corresponds to mass, length squared, and time inverse squared.” image-1=”” headline-2=”h3″ question-2=”What is the dimensional formula of electric potential Class 12?” answer-2=”The dimensional formula of electric potential is [M¹L²T⁻³I⁻¹], where it is derived from energy per unit charge​.” image-2=”” headline-3=”h3″ question-3=”What is the dimensional formula of voltage difference?” answer-3=”The dimensional formula of voltage difference is also [M¹L²T⁻³I⁻¹], as voltage represents potential difference between two points.” image-3=”” headline-4=”h3″ question-4=”What is the SI unit of potential difference and its dimensions?” answer-4=”The SI unit of potential difference is the volt (V), and its dimensional formula is [M¹L²T⁻³I⁻¹]” image-4=”” headline-5=”h3″ question-5=”Are voltage and potential difference the same?” answer-5=”Yes, voltage and potential difference refer to the same concept: the difference in electric potential between two points.” image-5=”” count=”6″ html=”true” css_class=””]