Dimensional Formula of Electromotive Force

Electromotive force is present in various electrical device cells, batteries, etc. This force does not operate like the ordinary force that we have learnt in mechanics. Inside an electrical device, different forms of energy like chemical energy in the case of batteries or mechanical energy in the case of a generator get converted to electrical energy to originate EMF. Electromotive force is a concept that can be defined in several ways for different electrical setups. For batteries, it is defined as the work done per unit positive charge.

In these notes of the Dimension formula of EMF (electromotive force), we will understand EMF from different perspectives and see the derivation of its dimensional formula.   

Dimensional Formula

A physical quantity’s dimensions are the powers to which the basic quantities are elevated to represent that amount. The dimensional formula of any physical quantity is an equation that explains how and which of the base quantities are contained in that amount. The dimensional formula is written by enclosing the symbols representing base amounts in square brackets with the corresponding power.

E.g., the dimensional formula of displacement is [L1].

A dimensional equation is obtained by equating a physical quantity with its dimensional formula.

In general, the total height of a wave is called its amplitude. According to physics, amplitude refers to the maximum dispersion of a point on a vibrating subject from its equilibrium point. As a result, the amplitude of a pendulum is one-half of the distance travelled by the bob as it moves from one side to the other. Waves are produced by vibrating sources, and their amplitude is proportional to the source’s amplitude.

Dimensional Formula of EMF (Electromotive Force)

According to the above definition, we can define electromotive force as

E =  W/C

Where, C = electric charge

 W = work done

So, the Dimensional formula of EMF = dimension of work done/dimension of electric charge

Now, W= F.S

So, the dimensional formula of W  = [MLT-2]x[L] = [ML2T-2]

So, the dimensional formula of  E = [ML2T-2]/ [IT] = [MI-1L2T-3] 

So, the dimensional formula of EMF is [MI-1L2T-3]

Definition of EMF (Electromotive Force) 

As mentioned above, the electromotive force basically originated from the interconversion of energy inside an electrical device. For batteries, it is defined as the work done to bring a unit positive charge from the low voltage side to the high voltage side internally. If ‘dq’ is the charge and ‘dw’ is the work done required to bring the charge, then the electromotive force becomes 

E = dw/dq

In the case of loops, EMF is defined as the work done to rotate a sample electric charge in the loop.  

Unit of EMF (Electromotive Force)  

In SI systems, the unit of EMF (Electromotive Force) is volt. It is the same unit used to measure electric potential. 

EMF (Electromotive Force) is a scalar quantity as only the value is measured, no direction is involved.  

Formula for EMF (Electromotive force)

ε = Ir+IR is the formula for the Electromotive force.

  = Ir+V

Where,

● ε is the EMF (electromotive force)

● r is the internal resistance of the cell

● I is the current across the circuit

● R is the external resistance

● V is the voltage of the cell

Therefore, the unit of electromotive force is volts.

Factors that affect induced EMF (Electromotive Force)

Some factors can affect the induced electromotive force. They are as follows:

● The induced electromotive force is proportionate to the number of bends in a coil.

● The velocity at which the conductor runs through the magnetic field.

● The size of the conductor.

● The velocity at which the conductor reduces the magnetic lines of force.

Characteristics of dimensional formula and equation

The dimensional formula and equation are based on the principle of homogeneity of dimensions. The principle can be used when all the physical quantities are of the same nature. All the dimensions used in physical quantities should have the same dimensions. These are the most important characteristics of dimensional formulas & equations. 

This principle checks the correctness of the physical equation. For example, if we have the power of 2 for all the terms like  L, M, T on the left side. The right side terms should also have the same power. Then, we can confirm that the physical equation is correct.

Conclusion 

In these notes of the dimensional formula of EMF (electromotive force), we learnt how to deduce the dimensional formula of EMF (Electromotive Force) and some basic concepts regarding this.

From the definition, one can see there is a similarity with electric potential. But they are different by nature. EMF is the cause, whereas electric potential is the effect. For electric potential, it happens due to the presence of EMF. It resists electrons of the lower voltage side of the battery to move towards the higher voltage side and keep the voltage difference unchanged.