Dimensional Formula of potential difference

Potential difference is the key to how current flows. Definition of electric potential says that the amount of work is needed to bring a positive unit charge from infinity. If there is a difference between the potential of two points, a potential gradient is generated.  

What is the potential difference?

Potential difference can be defined as the amount of work needed to take a unit charge from one point to the other. One of the two points has higher potential, and another is lower. Work needs to be done for a positive charge while taking from lower potential to a higher one.

Unit of potential difference: the SI unit for the potential difference is volt. 

Potential difference is a scalar quantity which means it only has magnitude but not direction. 

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 Galvanic cell electrodes is termed the cell potential. It is defined as the difference between the reduction potentials of the anode and cathode of the cell. This difference is measured in volts.

When no current is drawn from the cells, then the potential difference of the cells has termed the EMF. The EMF of a cell is positive and measured as the difference between the potential of the half cell on the right and the half cell on the left.

The EMF Formula:

Ecell = Eright – Eleft   ….. (eq1)

Cell reaction:

The copper electrode is the cell‘s anode, and the silver electrode is the cathode.

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

Here, (s) represents the electrode in solid form and (aq) represents it to be dissolved in water.

Potential difference and EMF of a half-cell

Measuring the cell’s potential can be done by measuring the difference of potential of the two half cells.

The half-cell reaction of the above cell reaction can be given as:

Cathode reduction of the silver electrode

2Ag+ (aq) + 2e- → 2Ag(s)  ……. (eq3)

Anode oxidation of the copper electrode

 Cu(s) → Cu2+ (aq) +2e-    ……..(eq4)

The summation of eq3 and eq4 results in the overall cell reaction from eq2. 

Eq1 can be represented in terms of the silver and copper electrode as:

Ecell = EAg+|Ag – ECu2+|Cu

Difference between cell potential and EMF

Conclusion :

In these notes, we discussed the Dimension formula for the potential difference in detail and how to drive the dimensional formula of potential difference. The potential difference of a cell is defined as the difference in reduction potential of the two electrodes of the cell, i.e. the cathode and the anode. The cathode is considered the positive end of the cell, and the anode is the negative end of the cell, as it releases electrons during the oxidation process. Electromotive Force or EMF of a cell can be defined as the potential difference of the cell when no current is drawn from the cell or the cell is in an open circuit. The potential difference measured between the two electrodes of a cell in a closed circuit is called the terminal potential difference of a cell.