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# Difference between EMF and Potential Difference

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The terminology ‘potential difference’ is a very comprehensive term and discovered in so many energy disciplines like electrical and magnetic fields, however, Electromotive Force (EMF) is solely used in the electric circuits. Though, both terms are measured in unit Volts (V), there are significant differences between them.

Electromotive force (EMF) can be described as the overall voltage in an electric circuit produced by the electric source. It is essentially the energy needed to actuate a positive charge from the negative to the positive terminal of the battery while the electric circuit is open.

EMF is basically measured in volts and represented by the letter E. Mathematically, it can be described as:

$E=I(R+r)$

Where R+r is a total external (circuit) and internal resistance (source) of the electric circuit.

The Potential Difference can be defined as the total work performed in order to actuate a charge between the negative terminal and the positive terminal of the source (battery).  The moment the electric circuit is closed (current starts flowing), a little portion of the EMF is spent in order to overcome the battery internal resistance. This energy per unit charge is known as potential difference.

Potential Difference is also measured in Volts and mathematically can be expressed as:

$V=E-Ir$

Where r is the battery internal resistance.

This article covers the key differences between EMF and Potential Difference on the basis of Circuit Resistance, Formulas, Magnitude, Current Flow, Representation, Operational Behavior, and Gain/Loss of Electric Energy.

## Difference between EMF and Potential Difference

CharacteristicsElectromotive Force (EMF)Potential Difference (PD)
DefinitionEMF is the utmost difference of potential between the two electrodes of the cell when no current is drawn off from the cell i.e. open circuitPD is the difference of potential between any two points in a closed electric circuit.
Resistance BehaviorIt does not depend on the circuit resistanceIt is directly related to the resistance between the two points of measurement.
Source Vs Circuit Term “EMF” is solely used for the source emf in the electric circuitIt is measured between any two points of a given electric circuit
FormulaFormula for EMF:
E=I(R+r)
Where
R+r= total external (circuit) and internal (source) resistance
Formula for PD:
V=E-Ir
Where
R= total external resistance ONLY
Magnitude of VoltageIt is the maximum voltage which we can achieve from the cell.It is ALWAYS less than the maximum voltage which can be obtained from the cell.
Current flow attributeResponsible for the constant current flow in the cell.Not responsible for the constant current flow in the cell.
RepresentationRepresented by letter ERepresented by letter V
Operational behaviorIt almost remains constantIt does not remain constant
Gain/Loss of Electric EnergyEMF identifies the gain in electric energy by electrons in an electric circuit.PD identifies a loss in electric energy by electrons as they move around the electric circuit.

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