Definition of Potential Difference as Potential of Electric Field

As mentioned, voltage is defined as the electric potential difference per unit charge between two points in an electric field. Let us describe this using equations.

Consider two points A and B.

The potential of point A with respect to point B is defined as the work done in moving a per unit charge from point A to B in the presence of electric field E.

Ezoic

Mathematically, this can be expressed as,

$\begin{align*} V_A_B = \frac{W}{Q} = -\int_B^A E^- * dl^-\end{align*}$

This is also a potential difference between points A and B with point B as a reference point. It can also be expressed as,

$\begin{align*} V_A_B = V_A - V_B \end{align*}$

Ezoic

Understanding the concept of voltage can be challenging.

So we’ll use an analogy to something tangible—something in the real world—to help make voltage easier to understand.

Understanding Voltage By Analogy

The “Hydraulic analogy” is a common analogy used to help explain voltage.

In the hydraulic analogy:

The voltage or electric potential is equivalent to hydraulic water pressure
Electric current is equivalent to hydraulic water flow rate
Electrical charge is equivalent to a quantity of water
An electrical conductor is equivalent to a pipe

Analogy 1

Consider a water tank as shown in the below figure. Figure (a) shows two tanks filled with the same water level. So, water can not flow from one tank to another tank as there is no pressure difference.

In Figure (b), two tanks have different water levels, creating a pressure difference that causes water to flow from one tank to the other until the levels equalize.

Similarly, if we connect two batteries through conducting wire with different voltage levels then charges can flow from the battery of higher potential to the battery of lower potential. As a result, the battery with lower potential charges until both batteries reach the same potential.

Analogy 2

Consider a water tank placed at a certain height above the ground. There is a hose at the bottom of the tank as shown in the below image.

Ezoic

The water pressure at the end of the hose is equivalent to the voltage or potential difference in an electric circuit. The water in the tank is equivalent to the electric charge. Now if we increase the amount of water in the tank then more pressure is developed at the end of the hose.

Conversely, if we drain a certain amount of water from the tank then the pressure created at the end of the hose will decrease. We can assume this water tank is like a storage battery. When the voltage of the battery decreases the lamps get dimmer.

Analogy 3

Let us understand how work can be done by voltage or potential difference in an electric circuit. A simple analogy between the hydraulic water circuit and the electric circuit is shown in the below figure.

Working Analogy of Hydraulic and Electric Circuit

As shown in the hydraulic water circuit, water flows through a pipe driven by a mechanical pump. A pipe is equivalent to conducting wire in an electric circuit.

Ezoic

Now, if a mechanical pump produces a pressure difference between two points, then pressurized water will be able to do work, such as driving a turbine.

Similarly, in an electric circuit, the potential difference of a battery can cause current to flow through the conductor hence, work can be done by flowing electric current, such as lighting the lamp.