Electric Potential and Potential Difference

In this article, we will study electric potential, potential difference, potential rise, and potential drop.

Electric Potential

Electric potential is defined as the ability of a charged body to do work. It is denoted by the symbol V and measured in volts.

In order to charge a body, some work is to be done. This work done is stored in the body in the form of potential energy. Now, the charged body can perform work by moving other charges either by attraction or repulsion. This capability of the charged body to perform work is termed as electric potential.

Mathematically, the electric potential (V) can be defined as the work done per unit charge, i.e.

`\V=("Work done "(W))/("Charge "(Q) )`

Where the work done is measured in Joules and the charge is measured in coulombs. Therefore, the unit of electrical potential can also be joules/coulomb.

`\∴1 "Volt"=1" Joule"⁄"Coulomb"`

To understand the concept of electric potential consider the following example:

If a charged body has an electric potential of 10 volts, it means that 10 joules of work have to be performed to charge the body to 1 coulomb.

Potential Difference

The potential difference is defined as the difference in the potentials of two charged bodies. The potential difference is also known as voltage. The SI unit of potential difference or voltage is also volts.

Consider two charged bodies X and Y having potentials of 10 volts and 20 volts respectively. 

It means that the per unit charge on the body X has a potential energy of 10 joules and the per unit charge on the body Y has a potential energy of 20 joules. Hence, body X has lower potential and body Y has higher potential.

If these bodies are joined together through a conducting wire, a difference in the potentials will exist between the ends of the wire. This difference in the potentials is termed as potential difference or voltage.

The potential difference causes the movement of charge or electrons. Thus, if there is no potential difference, no current will flow.

Mathematically, the potential difference between two charged bodies is given by,

`\V_{YX}=V_Y-V_X=-V_{XY}`

Note – The potential difference or voltage is always measured with respect to a point of reference, which means the voltage cannot be expressed at a single point. If we need to express the voltage of a single point, then the earth would be considered as the point of reference.

Potential Rise and Potential Drop

The potential rise and potential drop are also called as voltage rise and voltage drop respectively. A simple electric circuit consists of a voltage source and a resistor is shown in the following figure.

In any electric circuit if the electric current flows from a point of lower potential (or negative terminal) to a point of higher potential (or positive terminal) through an element, as in the case of the voltage source in the above circuit, then there is a rise in the potential associated with the element. Thus, the potential difference or voltage across the element is called voltage rise or potential rise.

If the direction of electric current through a circuit element is such that it flows from a higher potential point (positive terminal) to a lower potential point (negative terminal), then there is a decrease in the potential across the element. Hence, the voltage across the element is called as a voltage drop or potential drop. In the above circuit, the current through the resistor is from the positive to the negative terminal, thus there is a voltage drop across the resistor.

Note – A resistor always causes a voltage drop because it is a passive circuit component, hence cannot produce power, only consumes.