# Potential Difference

Potential refers to the possibility of doing work.  Any charge has the potential to do the work of moving another charge, by either attraction or repulsion. When we consider two unlike charges, they have a difference of potential.

A charge is the result of work done in separating electrons and protons.  Because of the separation, there is stress and strain associated with opposite charges, since normally they would be balancing each other to produce a neutral condition.  We could consider that the accumulated electrons are drawn tight and are straining themselves to be attracted toward protons in order to return to the neutral condition.  Similarly, the work of producing the charge causes a condition of stress in the protons, which are trying to attract electrons and return to the neutral condition.  Because of these forces, the charge of electrons or protons has potential, as it is ready to give back the work put into producing the charge.  The force between charges is in the electric field.

## Potential Between different Charges:

Potential always present in any type of charge, when one charge is different from the other, there must be a difference of potential between them. For instance, consider a positive charge of 3 C, as shown in figure (a), The charge has ca certain amount of potential, corresponding to the amount of work this charge can do.  The work to be done is moving some electrons, as illustrated.

Assume a charge of 1 C can move 3 electrons. Then the charge of +3 C can attract 9 electrons toward the right.  However, the charge of +1 C at the opposite side can attract 3 electrons toward the left. The net result, then, is that 6 electrons can be moved toward the right to the more positive charge.

In figure (b), one charge is 2 C, while the other charge is neutral with 0 C. For the difference of 2 C, again 2× 3 or 6 electrons can be attracted to the positive side.

In figure (c), the difference between the charges is still 2 C; the +1 C attracts 3 electrons to the right side. The –1 C repels 3 electrons to the right side also. This effect is really the same as attracting 6 electrons.

Therefore, the net number of electrons moved in the direction of the more positive charge depends on the difference of potential between the two charges.  The potential difference corresponds to 2 C for all three cases in below figures.  Potential difference is often abbreviated PD.

The only case without any potential difference between charges is where they both have the same polarity and are equal in amount.  Then the repelling and attracting forces cancel, and no work can be done in moving electrons between the two identical charges.

Note: French natural philosopher Charles Augustin Coulomb developed a method for measured the force of attraction and repulsion between two electrically charged spheres. Coulomb established the law of inverse squares and defined the basic unit of charge quantity, the coulomb.

## Unit of Potential Difference:

The Volt is the unit of potential difference; this unit is named after Alessandro Volta (1754-18257). Fundamentally, the volt is a measure of the work needed to more an electric charge.  When 0.7376 foot-pound (ft . lb ) of work is required to move 6.25×1018 electrons between two point each with its own charge, the potential difference is 1 V.

Note that 6.25×1018  electrons make up one coulomb.  Therefore the definition of a volt is for a coulomb of charge.

Also, 0.7376 ft. Lb of work is the same as 1 joule (j), which is the practical metric unit of work or energy.  Therefore, we can say briefly that one volt equals one joule of work per coulomb of charge, or

# 1V = 1 J / I C

The symbol for potential difference is V for voltage. In fact, the volt unit is used so after that potential difference is often called voltage. Remember, though, that voltage is the potential difference between two points.  Two terminals are necessary to measure a potential difference.

Consider the 2.2-V lead-acid cell as shown in below figure, its output of 2.2 V means that this is the amount of potential difference between the two terminals.  The cell then is a voltage source, or a source of electromotive force (emf).

Chemical cell as a voltage source (a) Voltage output is the potential difference between the two terminals. (b) Schematic symbol of any dc voltage source with constant polarity. Longer line indicates the positive side.

Sometimes the symbol E is used for emf, but the standard symbol is V for any potential difference. This applies either to the voltage generated by a source or to the voltage drop across a passive component, such as a resistor.

Note: In the practical circuit, the voltage determines how much current can be produced.