Potential Difference: Definition, Formula, Steps to Find, Example

Shashank Ranguwar

| Updated: Jun 30, 2022 10:52 IST

In the same way, when a charge is moved from one place to another its potential energy gets converted into the kinetic energy which is represented in terms of electric potential as \( KE = Q\times V \). Hence, the potential difference can be described as the change in potential energy and other forms of energy of a unit charge when it is moved from one point A to B in a circuit and the difference in the potential of these two points can be represented as \( V_{B}-V_{A} (\Delta V) = \Delta U/q \)

In this article, we will learn about the potential difference, the formula to calculate with steps, and the difference between potential difference and EMF along with the solved examples.

Potential Difference

Potential Difference also known as Voltage is defined as the work required per unit of charge to move a test charge between the two points. The SI unit of potential difference is Volt (V).

When current travels between two places P and Q in an electric circuit, we only consider the charge between the points P and Q, therefore knowing the precise potential at each point is not important. Knowing the possible difference between the two points does the job. As a result, the effort done in transporting a unit positive charge from one place to the other is equal to the potential difference between the two points. This process can also be clearly understood by the diagram given below.

Potential Difference

If the work involved in transferring a 1-coulomb charge from one location to another is 1 joule, the potential difference between the two points is said to be 1 volt.

1 volt= 1 joule/ 1 coulomb

The volt is the unit of measurement for potential difference, and the voltmeter is the equipment used to measure it. When attaching the voltmeter to the circuit, make sure the positive terminal is connected to the positive terminal of the cell and the negative terminal is connected to the negative terminal of the cell.

In terms of ohm’s law, the potential difference dropped across a fixed resistance of one ohm with a current of one ampere running across it is known as the Volt. In other words, one volt equals one ampere multiplied by one ohm or V = I×R

The term volt is given after the name of the physicist Alessandro Volta, who is credited for the invention of the electric battery.

Potential Difference Formula

The formula for calculating the potential difference is given as:

\( \delta v\ =\frac{\delta w}{\delta q} \)

Or,

\( V=\frac{W}{Q} \)

Where,

V = Potential Difference between the two points

W = Work Done to move the charge between these two points

Q = charge to be moved against electric field

The potential difference can be calculated in different terms. Let us discuss some other formulas for calculating the potential difference.

In terms of an electric field;

Since, \( E\ =\ \frac{F}{q} \)

and, \( W\ =\ Fdx \)

\( E\ =\ -\frac{\partial V}{\partial x} \)

Where,

E = electric field

dx = path length

dV = potential difference

Here, the negative sign represents the electric gradient

In terms of ohm’s law,

\( V\ =\ I\ \cdot\ R \)

Where,

I = current running across the resistor

R = Resistance

V = potential difference

Steps to find Potential Difference

According to the formulas given above, the potential difference can be calculated in two simple steps by each formula:

Step 1. Determine the work (W) required to move the charge (Q).

Step 2. Use the formula \( V\ =\ \frac{W}{Q}\) to calculate the potential difference.

Furthermore, the potential difference can also be calculated if the electrostatic force for the charge is given in the formula:

Step 1. Determine the work (W) by using \( W\ =\ Fd x \) and the charge.

Step 2. Use the formula \( V\ =\ \frac{W}{Q} \)or \(- \frac{d V}{dx} \) to calculate the potential difference.

Difference between the Potential difference and EMF

The difference between potential difference and EMF is as follows:

Potential Difference Electro-Motive Force (EMF)In a closed circuit, the difference of potential between any two points is termed as potential difference.The maximum potential difference between the two electrodes of the cell when the circuit is open i.e, no current is drawn from the cell.The energy dissipated as the unit charge flows through the components is known as the potential difference.It is defined as the energy supplied to the charge by the cell.The potential difference depends upon the resistance between two points in a directly proportional relationship.EMF does not change with the resistance in a circuit.The potential difference is always less in magnitude as compared to the EMF.The value of EMF is always greater than the potential differenceIt is induced under electric fields only.Electro-motive force can be generated in electric, magnetic and gravitational fields.The formula for voltage or potential difference is given as;

\( V\ =\ I\cdot R \)

Formula for EMF includes the internal resistance of the cell as well;

\( E\ =\ I\ \left(R\ +r\right) \)

Potential difference is considered as the effect of EMF.It is considered the cause of charge separation.

Potential Difference Solved Examples

Example 1. How much work is done in moving a charge of 4 coulombs across the two points having a potential difference of 2V?

Solution: Given,

Q = 4 C

V = 2 volt

W = ?

According to the formula;

\( W\ =\ Q\ \cdot V \)

\( W = 4\times 2 \)

W= 8 Joule

Example 2. What potential difference is required to do 120 J of work to carry a charge of 8 C between two points?

Solution: Given,

W = 120 J

Q = 8 C

V = ?

According to the formula;

\( W\ =\ Q\ \cdot V \)

V = 120/8

V = 15 volt

Example 3. The current of 6 amperes is flowing in wire for 1 minute when a potential difference of 10 volts is connected across it; calculate the work done during this process.

Solution: Given,
I = 6A

t = 60 s

V = 10 volt

W = ?

According to the relationships:

\( W\ =\ Q\ \cdot V \)

Q = It

W = VIt

\( W = 10 \times 6 \times 60 \)

W = 3600 J

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FAQs on Potential Difference

Q.1 What is the potential difference voltage?

Ans.1 In terms of ohm’s law, the potential difference dropped across a fixed resistance of one ohm with a current of one ampere running across it is known as the volt or voltage. In other words, one volt equals one ampere multiplied by one ohm or \( V=I\times R \).

Q.2 What is the potential difference between the two points?

Ans.2 It is the work done or energy released in the movement of a unit quantity of electrical charge from one point to another. This is represented by the difference in potential between these two points as \( V_{B}-V_{A} (\Delta V) = \Delta U/q \)

Q.3 What is the difference between current and potential difference?

Ans.3 Electric current is caused by the movement of ions or electrons within the wire, and it is the work required to transfer a unit positive charge from one location to another.

Q.4 Can the potential difference be negative?

Ans.4 Yes, the potential difference between two points could be negative or positive depending upon the connection of circuit terminals with the battery.

Q.5 Why is the potential difference useful?

Ans.5 It is useful in determining the amount of energy available to push the charges through the electrical circuit.

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