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Electric Potential, Potential Difference and EMF


Just as a body raised above the ground has gravitational potential energy, similarly, a charged body has electric potential energy. 

When a body is charged, work is done in charging the body. This work done is stored in the body in the form of electric potential energy. The charged body has the capacity to do work by moving other charges either by attraction or repulsion. 

Quantitatively, electric potential is defined as under :

The electric potential at a point is the electric potential energy per unit charge.

Electric Potential,  V  =  (Electric potential energy) / Charge = W/Q

The SI unit of energy or work is 1 J and that of charge is 1 C so that SI unit of electric potential is 1 J/C which is also called 1 volt.

Thus when we say that electric potential at a point is 10 V, it means that if we place a charge of 1C at that point, the charge will have electric potential energy of 10 J. 
Similarly. if we place a charge of 2 C at that point, the charge will have electric potential energy of 20 J. Note that potential energy per unit charge (i.e electric potential) is 10 V.

Potential Difference

The difference in the potentials of two charged bodies is called potential difference (pd). 


Consider two bodies A and B having potentials of +5 V and +3 V respectively as shown in figure 1 below. Each coulomb of charge on body A has an energy of 5 Joules while each coulomb of charge on body B has an energy of 3 Joules. Clearly, the body A is at higher potential than body B.


If the two bodies are joined through a conducter [see figure 2 above], then eleetrons will flow from body B to body A ( The conventional electric current will be in opposite direction i.e. from A to B). 


When the two bodies attain the same potential, the flow of current stops. Therefore, we arrive at a very important conclusion that current will flow in a circuit if potential difference exists. No potential difference, no current flow. It may be noted that potential difference is sometimes called voltage.

Unit of Potential Difference

Since the unit of electric potential is volt, one can expect that the unit of potential difference will also be volt. It is defined as :

The potential difference between two points is 1 Volt if one joule of work is done in transferring l C of charge from the point of lower potential to the point of higher potential.

Consider points A and B in an electrical circuit as shown in figure above. Suppose VA = VB = 1 Volt. It means that 1 J of work will be done in transferring l C of charge from point B to point A. 


Alternatively, 1 J of work (or energy) will be released (as heat) if 1 C of charge moves from point A to point B. Note that volt is the unit of energy.

Concept of EMF and Potential Difference

There is a distinct difference between e.m.f. and potential difference. 


The e.m.f. of a device, say a battery, is a measure of the energy the battery gives to each coulomb of charge. Thus if a battery supplies 4 joules of energy per coulomb, we say that it has an e.m.f. of 4 volts. The energy given to each coulomb in a battery is due to the chemical action.

The potential difference between two points, say A and B, is a measure of the energy used by one coulomb in moving from A to B. Thus if potential difference between points A and B is 2 volts, it means that each coulomb will gave up an energy of 2 joules in moving from A to B.

Fundamental Differences between EMF and Potential Difference

The following are the differences between e.m.f. and p.d. :

  • The name EMF at first sight implies that it is a force that causes current to flow. But this is not correct because it is not a force but energy supplied to charge by some active device such as a battery.

  • EMF maintains p.d. while p.d. causes current to flow.

  • When we say that EMF of a device (e.g., a cell) is 2 V, it means that the device supplies an energy of 2 joules to each coulomb of charge. When we say that a p.d. between points A and B of a circuit (suppose point A is at higher potential) is 2 V. it means that each coulomb of charge will give up an energy of 2 joules in moving from A to B.